# How do you find an equation of the tangent line to the curve at the given point: #y=(2x)/(x+1)^2# at point (0,0)?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the equation of the tangent line to the curve at the point (0,0), we need to find the derivative of the function y=(2x)/(x+1)^2 and evaluate it at x=0. The derivative of the function is given by the quotient rule, which states that the derivative of (f(x)/g(x)) is (f'(x)g(x) - f(x)g'(x))/(g(x))^2. Applying the quotient rule to the given function, we get:

y' = [(2(x+1)^2 - 2x(2(x+1))]/((x+1)^2)^2

Simplifying this expression, we have:

y' = [2(x+1)^2 - 4x(x+1)]/[(x+1)^2]^2

Evaluating this expression at x=0, we get:

y'(0) = [2(0+1)^2 - 4(0)(0+1)]/[(0+1)^2]^2

Simplifying further, we have:

y'(0) = [2(1) - 4(0)]/[1]^2

y'(0) = 2/1

y'(0) = 2

Therefore, the slope of the tangent line at the point (0,0) is 2.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values x1=0, y1=0, and m=2 into the equation to find the equation of the tangent line:

y - 0 = 2(x - 0)

Simplifying this equation, we have:

y = 2x

Therefore, the equation of the tangent line to the curve y=(2x)/(x+1)^2 at the point (0,0) is y = 2x.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

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.

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.

- What is the equation of the line tangent to # f(x)=x^2+6x-5# at # x=3 #?
- What is the equation of the tangent line of #f(x) =((x-1)^3(x^2+2))/(e^x-1)^4# at #x=2#?
- What is the equation of the normal line of #f(x)=xln(3^(1/x))# at #x=0#?
- What are the x-values on the graph of #y= 1/x# where the graph is parallel to the line #y= -4/9x+7#?
- What is the equation of the normal line of #f(x)= x^3/(3x^2-2x)+6x# at #x = 2#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7