How do you find the derivative of root3((6x+7))3(6x+7)?

1 Answer
Nov 4, 2016

Use the chain rule.

Explanation:

First, recognize that you are looking at the cube root of (6x + 7)(6x+7), which can be rewritten as (6x+7)^(1/3)(6x+7)13. Then you will need to use the chain rule to take the derivative.

To do this, you would first bring down the power of 1/313 and reduce the power by one. This results in 1/3(6x+7)^(-2/3)13(6x+7)23. Then, multiply this by the derivative of the term inside the parentheses, which is just 6 (the derivative of a constant is zero).

Your final simplified answer is 2(6x+7)^(-2/3)2(6x+7)23.