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How do you find #(d^2y)/(dx^2)# given #y=root3(x)#?

Answer 1

Christopher Allers

#(d^2y)/dx^2 = -2/(9x^(5/3))#

The notation #(d^2y)/dx^2# means to find the 2nd derivative.

So, we differentiate once, and we differentiate that result again.

#y = root(3)(x) -> y = x^(1/3)#

#y' = 1/3x^(-2/3) #

The second derivative is found by differentiating the first derivative.

#y'' = 1/3(-2/3)x^(-5/3) = -2/9x^(-5/3) = -2/(9x^(5/3))#

Hopefully this helps!

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Answer 2

Evelyn Agard

To find the second derivative (d^2y)/(dx^2) given y = √3x:

Find the first derivative of y with respect to x, which is dy/dx.
Differentiate dy/dx with respect to x to find the second derivative.

Let's go through the steps:

First derivative of y = √3x: dy/dx = (d/dx)(√3x) = √3 * (d/dx)(x) = √3
Second derivative of y with respect to x: (d^2y)/(dx^2) = (d/dx)(dy/dx) = (d/dx)(√3) = 0

So, the second derivative of y = √3x with respect to x is 0.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.