Answer
$(8x-1)^{1/3} (x-1)(\dfrac{8}{24x-3}+\dfrac{1}{x-1}) $
Work Step by Step
We have: $y=(8x-1)^{1/3} (x-1)$
We differentiate both sides with respect to $x$.
$\ln y=\dfrac{1}{3}\ln (8x-1) +\ln (x-1) \\ \dfrac{d}{dx}(\ln y)=\dfrac{1}{3} (\dfrac{8}{8x-1})+\dfrac{1}{x-1} \\ \dfrac{dy}{dx}=y(\dfrac{8}{24x-3}+\dfrac{1}{x-1}) \\ \dfrac{dy}{dx}=(8x-1)^{1/3} (x-1)(\dfrac{8}{24x-3}+\dfrac{1}{x-1}) $
