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

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Answer 1 · 2017-05-10T14:07:37

#f'(x)=(3+x)e^x#

Let's assume that you meant to ask how differentiate
#f(x)=(2+x)e^x#

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

In the given equation, let #g(x)=2+x# and #h(x)=e^x#

The derivatives are #g'(x)=1# and #h'(x)=e^x#

Plugging all four into the product rule gives

#f'(x) =(2+x)e^x+e^x=(3+x)e^x#