How do you differentiate #f(x)=xe^2-x# using the product rule?

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Answer 1 · 2015-11-19T14:06:37

Actually, there's no need to use the product rule here: you have written #x(e^2-1)#, and you can derive it to get #e^2-1# immediately.

Maybe there's a mistake and you meant #x*e^x#?

In that case, the product rule states that

#(f*g)' = f'g+fg'#

So, we have

#f'g+fg'=1*e^x + x*e^x = e^x(1+x)#

And the whole derivative would thus be #e^x(1+x)-1#