Answer
$\displaystyle \frac{dy}{dx}=5x^{4}-6x^{5}$
Work Step by Step
Set:
$f(x)=x^{5}\ \ \quad g(x)=1-x$
$f^{\prime}(x)=5x^{4}\qquad g^{\prime}(x)=0-1=-1$
$\displaystyle \frac{dy}{dx}=\frac{d}{dx}[f(x)g(x)]$= ... product rule ...
$= f^{\prime}(x)g(x)+f(x)g^{\prime}(x)$
$=5x^{4}(1-x)+x^{5}(-1)$
$=5x^{4}-5x^{5}-x^{5}$
$=5x^{4}-6x^{5}$
