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))`

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))`