`f(x) = ((x^2 + 3)^5 + x)^2` Find the derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 33 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to find derivative of the function using the chain rule:

`f'(x)= (((x^2+3)^5+x)^2)'*((x^2+3)^5+x)'`

`f'(x)= (2((x^2+3)^5+x))*(5(x^2+3)^4*(x^2+3)'+1)`

`f'(x)= (2((x^2+3)^5+x))*(10x(x^2+3)^4+1)`

Hence, evaluating the derivative of the function, yields` f'(x)= (2((x^2+3)^5+x))*(10x(x^2+3)^4+1).`

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