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

Expert Answers
sciencesolve eNotes educator| Certified Educator

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).`