Did I do this Exponential Function correctly...?????

Question

Find f'(x).

f(x) = xe^(-2x)



This is what I did:

u = x
du = 1
v = e^(-2x)
dv = -2e^(-2x)

(x) (-2e^(-2x)) + (e^(-2x)) (1)

That got me:
-2xe^(-2x) + e^(-2x)


Is that correct?

Answer 1

Absolutely correct!!
Perfect application of the product rule.

The only thing I would change is in your answer, start with
f '(x) = ...
so that it's clear what you have in mind.

Answer 2

It is correct