Answer
$\displaystyle \frac{(1-4x^{3})\cdot|x-x^{4}|}{x-x^{4}}$
Work Step by Step
With $u(x)=x-x^{4}$,
$\displaystyle \frac{du}{dx}=1-4x^{3},$
apply the Generalized Power Rule (see table on p.823)
$\displaystyle \frac{d}{dx}|u|=\frac{|u|}{u}\frac{du}{dx}$
$\displaystyle \frac{d}{dx}|x-x^{4}|=\frac{|x-x^{4}|}{x-x^{4}}\cdot(1-4x^{3})$
$=\displaystyle \frac{(1-4x^{3})\cdot|x-x^{4}|}{x-x^{4}}$
