`f(s) = (s^2 - 1)^(5/2) (s^3 + 5)` Find the derivative of the function.

Textbook Question

Chapter 2, Review - Problem 62 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

`f(s)=(s^2-1)^(5/2)(s^3+5)`

Using the product rule for the derivative,

`f'(s)=(s^2-1)^(5/2)d/(ds)(s^3+5)+(s^3+5)d/(ds)(s^2-1)^(5/2)`

`f'(s)=(s^2-1)^(5/2)(3s^2)+(s^3+5)(5/2)(s^2-1)^((5/2)-1)(2s)`

`f'(s)=3s^2(s^2-1)^(5/2)+5s(s^2-1)^(3/2)(s^3+5)` 

`f'(s)=s(s^2-1)^(3/2)(3s(s^2-1)+5(s^3+5))`

`f'(s)=s(s^2-1)^(3/2)(3s^3-3s+5s^3+25)`

`f'(s)=s(s^2-1)^(3/2)(8s^3-3s+25)`

We’ve answered 318,994 questions. We can answer yours, too.

Ask a question