Question

find the first and second derivative of:

f(x) = (x+2)/e^x


I get to:

f'(x) = e^x - (x+2)(e^x) / (e^x)^2

I'm stuck at that

Answer 1

I think the quotient rule gets bogged down here. Use the product rule with a negative exponent:

y = (x+2)e^-x

y' = e^-x - (x+2)e^-x
= -(x+1)e^-x

y'' = -e^-x + (x+1)e^-x
= xe^-x

However, using your quotient rule, factor out the ex top and bottom:

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

Do it again, and you wind up where I did.

Answer 2

Tnx for the quick answer, but I still have a question:

why is it - in y' = e^-x (-) (x+2)e^-x
instead of a + ?

Answer 3

and how do you get (x+1)?

Answer 4

oh I get it now, tnx!