How do you find the derivative of #(x^2)(e^x)#?

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Answer 1 · 2018-07-27T22:13:20

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

Let #f(x)=x^2# and #g(x)=e^x#. Since we have a product of functions, the derivative can be found with the Product Rule

#f'(x)g(x)+f(x)g'(x)#

From some basic derivatives, we know #f'(x)=2x# and #g'(x)=e^x#. We can now plug these into the Product Rule to get

#2xe^x+x^2e^x#

We can factor out an #e^x# to get

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

Hope this helps!