Question

How do you differentiate `g(x) = (2 -e^x) ( 2x-x^2)` using the product rule?

Answer 1

`g(x)=x^2e^x-2e^x-4x+4`

Explanation:

Using the product rule

`(uv)'=u'v+uv'`
we get

`g'(x)=-e^x(2x-x^2)+(2-e^x)(2-2x)`

expanding we get

`g'(x)=-2xe^x+x^2e^x+4-2e^x-4x+2xe^x`

`g'(x)=x^2e^x-2e^x-4x+4`