How do you differentiate #f(x)=(x^2-2x+1)(x^3-1)# using the product rule?

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Answer 1 · 2017-12-29T10:40:25

#5x^4-8x^3+3x^2-2x+2#

Product Rule #color(red)(=f'(x)g(x)+f(x)g'(x))#

In our case, #f(x)=x^2-2x+1# and #g(x)=x^3-1#

Substitute:

#=d/dx(x^2-2x+1)(x^3-1)+(x^2-2x+1)d/dx(x^3-1)#

Differentiate:

The Power Rule tells us that #d/dx x^n=nx^(n-1)#

#=(2x-2)(x^3-1)+(x^2-2x+1)(3x^2)#

Expand:

#=(2x^4-2x^3-2x+2) + (3x^4-6x^3+3x^2)#

Simplify:

#=5x^4-8x^3+3x^2-2x+2#