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

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Answer 1 · 2017-03-07T17:41:17

#=3xe^x+x^2e^x+e^x-6x^2-4x#

The product rule states that:

#f(x)=g(x)*h(x)->f'(x)=g'(x)*h(x)+g(x)*h'(x)#

Then it is:

#f'(x)=(2x+1)* (e^x-2x)+(x^2+x)*(e^x-2)#

#=2xe^x-4x^2+e^x-2x+x^2e^x-2x^2+xe^x-2x#

Let's sum the like terms:

#=3xe^x+x^2e^x+e^x-6x^2-4x#