How do you find the second derivative of #z=(x-5)/(x+2)#?

Question

Emily Ammerman · Accepted Answer

#(d^2z)/dx^2 = -14/(x+2)^3 #

Calculate the first derivative using the quotient rule:

#(dz)/dx = ((x+2)d/dx(x-5) -(x-5)d/dx(x+2))/(x+2)^2#

#(dz)/dx = (x+2 -x+5)/(x+2)^2 = 7/(x+2)^2#

Then using the chain rule:

#(d^2z)/dx^2 = d/dx (7/(x+2)^2) = -14/(x+2)^3 d/dx (x+2) = -14/(x+2)^3 #

Alternatively you can write the function as:

#z= (x-5)/(x+2) = (x+2-7)/(x+2) = 1-7/(x+2) = 1-7(x+2)^-1#

and you can see that:

#(d^nz)/dx^n = 7(-1)^(n+1)(n!)/(x+2)^(n+1)#

William Abdalla · Answer

#(d^2z)/dx^2=(-14)/(x+2)^3#

One way is to express the function as a product and differentiate using the product rule.

#rArrz=(x-5)/(x+2)=(x-5)(x+2)^-1#

differentiate using the #color(blue)"product rule"#

#"Given "z=g(x)h(x)" then"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(dz/dx=g(x)h'(x)+h(x)g'(x))color(white)(2/2)|)))#

#rArrdz/dx=(x-5).-1(x+2)^-2+(x+2)^(-1).1#

#"to obtain "(d^2z)/(dx^2)" differentiate " dz/dx#

differentiate the first term using the #color(blue)"product rule"#

#rArr(d^2z)/(dx^2)=(x-5).2(x+2)^-3-(x+2)^(-2).1-(x+2)^-2#

#=2(x-5)(x+2)^-3-2(x+2)^-2#

#=2(x+2)^-3(x-5-x-2)#

#=-14/(x+2)^3#

Christopher Agresta · Answer

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1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

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1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z \To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

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1. Find the first derivative of $ z $ with respect to $ x $.
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First, let's find the first derivative of $ z $:

To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

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First, let's find the first derivative of $ z $:

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1. Find the first derivative of $z$ with respect to $x$.
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First, let's find the first derivative of $ z $:

\[ z =To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

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1. Find the first derivative of $ z $ with respect to $ x $.
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First, let's find the first derivative of $ z $:

\[ z = \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{xTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(xTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x +To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{xTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1)To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2}To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (xTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x -To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ zTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z'To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' =To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \fracTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(xTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x +To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x +To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(xTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 -To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x +To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - xTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x +To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}\To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$zTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' =To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x +To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(xTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(xTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x +To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x +To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}\To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2}To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

NowTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now,To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, forTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z'To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' =To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$zTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z''To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' =To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x +To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{dTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dxTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2}To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \leftTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

NowTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\fracTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now,To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, letTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's findTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(xTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivativeTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' =To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\rightTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)\To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \fracTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{dTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using theTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dxTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotientTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx}To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left(To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$zTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z''To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \fracTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \fracTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(xTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((xTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x +To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x +To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2)To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \rightTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ zTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x +To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' =To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \fracTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{dTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(xTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(xTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \rightTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x +To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right)To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) \To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ zTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x +To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' =To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

\[z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(xTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivativeTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x +To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative ofTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ zTo find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z \To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

\[ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ withTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

SoTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect toTo find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, theTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ xTo find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the secondTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x \To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivativeTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $To find the second derivative of \( z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $zTo find the second derivative of \( z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $ -To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $z$To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $ -14To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $z$ withTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $ -14(xTo find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $z$ with respect toTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $ -14(x + To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $z$ with respect to $To find the second derivative of \( z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $ -14(x + 2To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $z$ with respect to $xTo find the second derivative of \( z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $ -14(x + 2)^To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $z$ with respect to $x$ isTo find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $ -14(x + 2)^{-To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $z$ with respect to $x$ is \To find the second derivative of $ z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $ -14(x + 2)^{-3To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $z$ with respect to $x$ is $\To find the second derivative of \( z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $ -14(x + 2)^{-3} \To find the second derivative of the function \(z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $z$ with respect to $x$ is $\frac{-14To find the second derivative of \( z = \frac{x - 5}{x + 2} $, follow these steps:

1. Find the first derivative of $ z $ with respect to $ x $.
2. Once you have the first derivative, find the derivative of that result with respect to $ x $. This second derivative will be the result.

First, let's find the first derivative of $ z $:

$$ z = \frac{x - 5}{x + 2} $$

$$ z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2} $$

$$ z' = \frac{x + 2 - x + 5}{(x + 2)^2} $$

$$ z' = \frac{7}{(x + 2)^2} $$

Now, let's find the second derivative:

$$ z'' = \frac{d}{dx} \left( \frac{7}{(x + 2)^2} \right) $$

$$ z'' = \frac{d}{dx} \left( 7(x + 2)^{-2} \right) $$

$$ z'' = -14(x + 2)^{-3} $$

So, the second derivative of $ z $ with respect to $ x $ is $ -14(x + 2)^{-3} $.To find the second derivative of the function $z = \frac{x - 5}{x + 2}$, follow these steps:

1. Find the first derivative of $z$ with respect to $x$.
2. Differentiate the expression obtained in step 1 with respect to $x$ to find the second derivative.

Starting with step 1:

$$z = \frac{x - 5}{x + 2}$$

$$z' = \frac{(x + 2)(1) - (x - 5)(1)}{(x + 2)^2}$$

$$z' = \frac{x + 2 - x + 5}{(x + 2)^2}$$

$$z' = \frac{7}{(x + 2)^2}$$

Now, for step 2:

$$z'' = \frac{d}{dx} \left(\frac{7}{(x + 2)^2}\right)$$

Using the quotient rule:

$$z'' = \frac{(0)((x + 2)^2) - 7(2(x + 2))}{(x + 2)^4}$$

$$z'' = \frac{-14(x + 2)}{(x + 2)^4}$$

$$z'' = \frac{-14}{(x + 2)^3}$$

So, the second derivative of $z$ with respect to $x$ is $\frac{-14}{(x + 2)^3}$.