Question

can someone walk me through the steps to finding the derivative of e^-x ????

Answer 1

Hint: let u = -dx

find the derivative of that then use u-sub..tell me what you get

Answer 2

i thought that the derivative of e^x is e^x?

Answer 3

oh wait...let u = -x

Answer 4

wouldn't that mean that the derivative of e^-x is e^-x?

Answer 5

lol..i was thinking of something but wrote the wrong thing...

let u = -x

take the derivative of that then use u-sub

Answer 6

so then it would be e^u u', which is e^-x*-1?

Answer 7

wait...what did you do?

let u = -x
du = -dx

you need dx so only so divide both sides by -1

\(\int e^{-x}dx = -\int e^u du\)

you get what im pointing out?

Answer 8

Yeah i just came up with it in a little different way. By using implicit differentiation I thought f'(u) *u' if I am remembering how that went correctly

Answer 9

i dont know what that means sorry =)) so do you know how to integrate \( -\int e^u du\) now?

Answer 10

yes but I was trying to differentiate it. Close enough though, I do get the point now, thank you

Answer 11

oh you mean thinking of something that when taken the derivative results to e^-x huh....well if you take the derivative of e^-x..it's e^-x(-1) because you need to take the derivative of -x accdg to chain rule