How do you find the derivative of xe^{x}?

[danielle36]

I came across a derivative question on my exam that involved finding the derivative of

$$xe^{x}$$

and I realized I wasn't sure what to do with it... I figured you could either use

$$f'(x^{n}) = nx^{n-1}$$

and come out with

$$xe^{x}$$

or maybe since x is a variable you need to use the multiplication rule?

f'g + g'f

$$= e^{x} + xe^{x}$$

(Or maybe something entirely different - this is still new to me )

 

[838]

You answered your own question. You use the product rule and come out with xe^x+e^x. Good job.

EDIT: Some teachers would prefer you to simplify your problem into (x+1)e^x, but either way, you got the right answer.