How do you differentiate #f(x)= x^3(2x - 2)# using the product rule?

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Answer 1 · 2015-12-05T01:51:29

#f'(x)=8x^3-6x^2#

According to the product rule:

#f'(x)=(2x-2)d/dx[x^3]+x^3d/dx[2x+2]#

Find each derivative separately.

#d/dx[x^3]=3x^2#

#d/dx[2x-2]=2#

Plug back in.

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

#f'(x)=6x^3-6x^2+2x^3#

#f'(x)=8x^3-6x^2#

Note that there's an easier way to do this, but it doesn't use prodyct rule:

Distribute the #x^3# term first.

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

#f'(x)=8x^3-6x^2#