`f(x) = root(3)(12x - 5)` Find the derivative of the function.

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Chapter 2, 2.4 - Problem 16 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: `f(x)=root(3)(12x-5)`

Rewrite the function as `f(x)=(12x-5)^(1/3)`

Find the derivative by using the Chain Rule.

`f'(x)=(1/3)(12x-5)^(-2/3)(12)`

`f'(x)=4(12x-5)^(-2/3)`

`f'(x)=4/(12x-5)^(2/3)`

`f'(x)=4/(root(3)((12x-5)^2))`

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