# What is the derivative of f(x) = x(2-x)^2?

$f \left(x\right) = x \left(4 - 4 x + {x}^{2}\right) = {x}^{3} - 4 {x}^{2} + 4 x$
$\implies \textcolor{b l u e}{f ' \left(x\right) = 3 {x}^{2} - 8 x + 4}$