What is the derivative of y=(2x+1)^2((x^2+5)/(x^2-2))?

1 Answer
JereJK .
Mar 5, 2018

(2(2x+1)*(2))*((-14x)/(x^2-2)^2)

Explanation:

To begin, you want to use the chain rule for the first portion

(2x+1)^2

The chain rule is done by finding the derivative of the outside, keeping the inside, and after that you will multiply it by the derivative of the inside.

f'(g(x)) * g'(x)

This will give us

2(2x+1)*(2)

Next you want to find the derivative of the next function using the quotient rule.

((f'(x)g(x))-(f(x)g'(x)))/(g(x))^2

It will look like

(((2x)*(x^2-2))-((x^2+5)*(2x))) / (x^2-2)^2

After you simplify it should look like

((2x^3-4x)-(2x^3+10x))/(x^2-2)^2

Then you end up with

(-14x)/(x^2-2)^2

Finally you can combine the two to get your final answer

(2(2x+1)*(2)) * ((-14x)/(x^2-2)^2)

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