Question

what is the derivative and second derivative of xe^-x?

Answer 1

product rule:
if f = u.v, then f' = u.v' + u'.v where u = x & v = e^-x

Answer 2

I got it! Thanks!

Answer 3

let A = xe^-x
take log both side,
ln(A) = ln( xe^-x)
ln(A) = lnx - xln(e), since lne =1
lnA = lnx - x
now differentiate both side
(1/A)A' = 1/x - 1
A' = ((1-x)/x)A
A' = (1-x)e^-x

Answer 4

That's what I got too! :)