Answer
$\displaystyle \frac{dy}{dx}=\frac{8}{(5x-2 )^{2}}$
Work Step by Step
$f(x)=4x\displaystyle \ \ \quad g(x)=5x-2\quad y=\frac{f(x)}{g(x)}$
$f^{\prime}(x)=4\qquad g^{\prime}(x)=5$
$\displaystyle \frac{dy}{dx}=\frac{d}{dx}[\frac{f(x)}{g(x)}]$= ... quotient rule ...
$= \displaystyle \frac{f^{\prime}(x)g(x)-f(x)g^{\prime}(x)}{[g(x)]^{2}}$
$=\displaystyle \frac{4(5x-2 ) - 4x(5)}{(5x-2 )^{2}}$
$=\displaystyle \frac{20x-8-20x}{(5x-2 )^{2}}$
$= \displaystyle \frac{8}{(5x-2 )^{2}}$
