Question

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

Answer 1

I found: `f'(x)=(1-x)^2(1-4x)`

Explanation:

You can try the Product Rule and the Chain Rule (to deal with `()^3`) to get:
`f'(x)=1*(1-x)^3+3x(1-x)^2*(-1)=`
`=(1-x)^3-3x(1-x)^2=(1-x)^2(1-x-3x)=`
`=(1-x)^2(1-4x)`