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

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

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Answer 1 · 2015-07-07T21:59:35

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)#

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

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