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

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Answer 1 · 2018-07-14T18:28:42

$g (x) = x^{2} e^{x} - 2 e^{x} - 4 x + 4$ $g(x)=x^2e^x-2e^x-4x+4$

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

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

expanding we get

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

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

How do you differentiate g(x) = (2 -e^x) ( 2x-x^2)g(x)=(2−ex)(2x−x2)g(x) = (2 -e^x) ( 2x-x^2) using the product rule?