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

1 Answer
Morgan
Nov 4, 2016

Use the chain rule.

Explanation:

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

To do this, you would first bring down the power of #1/3# and reduce the power by one. This results in #1/3(6x+7)^(-2/3)#. 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)#.

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