How Do You Apply the Product Rule to Differentiate uxe^-x?

[jackalope1234]

Homework Statement

I need to differentiate uxe^-x in order to do a reduction order question.

Homework Equations

d/dxf(x)g(x) = f(x)g'(x) + g(x)f'(x) <--- that's the product rule about 2 variable

The Attempt at a Solution

I would assume
y' = -uxe^-x + u'xe^-x

I was told elsewhere you would consider the ux as a single unit as opposed to the u and xe^-x though resulting in
-uxe^-x + ue^-x

any help would be appreciated.

 

[tiny-tim]

welcome to pf!

hi jackalope1234! welcome to pf!

general rule: (ABC)' = A'BC + AB'C + ABC'

(because it's (AB)'C + (AB)C')

 

[jackalope1234]

I assumed "general rule: (ABC)' = A'BC + AB'C + ABC' " would be the method thank you for confirming. thank you for the welcome, maybe this forum will pull me away from starcraft 2 :D.