Answer
$f'(x)=6 (3x^2+2x-1)^5 (6x+2) $
Work Step by Step
Given that $f(x)=(3x^2+2x−1)^6$
We can write this as $ f (x)=(g (x))^6$, where $ f (x)$ is the outside function and $ g ( x ) = 3x^2+2x-1$ is the inside function.
To find the answer we need to differentiate the outside function $ f(x) $ and times it by the derivative of the inside function $ g (x)$.
$f(x)=(3x^2+2x−1)^6$
$ f (x)=(g (x))^6$
$f'(x)=6(g ( x ))^{6-1}×(g' ( x )) $
$f'(x)=6(g ( x ))^{5}×(6x^{2-1}+2) $
$f'(x)=6(3x^2+2x−1)^{5}×(6x^{1}+2) $
$f'(x)=6(3x^2+2x−1)^{5}(6x+2) $
