`f(x) = 2/(root(3)(x)) + 3cos(x)` Find the derivative of the function.

Textbook Question

Chapter 2, 2.2 - Problem 52 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

kalau's profile pic

kalau | (Level 2) Adjunct Educator

Posted on

The first term is the same as:

`2/x^(1/3) =2x^(-1/3)`

Take the derivative of this term.

`-1/3(2)x^(-1/3-1) = -2/3x^(-4/3)`

The derivative of `3cos(x)` is `-3sin(x)` .  

Combine the terms.

`f'(x)=-2/3x^(-4/3)-3sin(x)` 

Rewrite the first term to eliminate the negative exponent.

The answer is:

`f'(x)=-2/(3x^(4/3))-3sin(x)`

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question