Answer
$\displaystyle \frac{5|5x-1|}{5x-1}$
Work Step by Step
With $u(x)=-5x+1$,
$\displaystyle \frac{du}{dx}=-5,$
apply the Generalized Power Rule (see table on p.823)
$\displaystyle \frac{d}{dx}|u|=\frac{|u|}{u}\frac{du}{dx}$
$\displaystyle \frac{d}{dx}|-5x+1|=\frac{|-5x+1|}{-5x+1}\cdot(-5)$
$=\displaystyle \frac{-5|-5x+1|}{-(5x-1)}$
$=\displaystyle \frac{5|-(5x-1)|}{5x-1}=\frac{5|-1|\cdot|5x-1|}{5x-1}$
$=\displaystyle \frac{5|5x-1|}{5x-1}$
