What is the derivative of #xe^x#?

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Answer 1 · 2014-12-17T17:45:57

To evaluate this derivative you use the product rule .

When you have a function that is the product of 2 functions #f(x)# and #g(x)# you can derive it as:

#d/(dx)f(x)g(x)=f'(x)g(x)+f(x)g'(x)#

In your case:

#f(x)=x and f'(x)=1#
#g(x)=e^x and g'(x)=e^x#

Finally deriving the complete function we have:

#d/(dx)xe^x=1e^x+xe^x=e^x(x+1)#