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

##### 1 Answer

Dec 16, 2016

No product rule is required if one simply expands the quadratic.

#f(x) = x(4 - 4x + x^2) = x^3 - 4x^2 + 4x#

#=> color(blue)(f'(x) = 3x^2 - 8x + 4)#

via the power rule.