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Question #36999

1 Answer

Jul 18, 2017

#g'(x)=e^x(x^2+2x)#

#g''(x)=e^x(x^2+4x+2)#

Explanation:

We will use the product rule.

#g'(x)=(x^2)'e^x+x^2(e^x)'=2xe^x+x^2e^x=e^x(x^2+2x)#

#g''(x)=(e^x)'(x^2+2x)+e^x(x^2+2x)'=#

#e^x(x^2+2x)+e^x(2x+2)=e^x(x^2+4x+2)#

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