# How do you find the derivative for f(x)= x(1-x)^3?

Jul 7, 2015

I found: $f ' \left(x\right) = {\left(1 - x\right)}^{2} \left(1 - 4 x\right)$

#### Explanation:

You can try the Product Rule and the Chain Rule (to deal with ${\left(\right)}^{3}$) to get:
$f ' \left(x\right) = 1 \cdot {\left(1 - x\right)}^{3} + 3 x {\left(1 - x\right)}^{2} \cdot \left(- 1\right) =$
$= {\left(1 - x\right)}^{3} - 3 x {\left(1 - x\right)}^{2} = {\left(1 - x\right)}^{2} \left(1 - x - 3 x\right) =$
$= {\left(1 - x\right)}^{2} \left(1 - 4 x\right)$