Question

can someone help me with this derivative problem:

f(x) = x/e^x

answer in the book is: y' = (1-x)/e^x

Answer 1

they did a bit of simplification i guess

Answer 2

best bet is to write this as \(xe^{-x}\) and use the product rule, although you can use the quotient rule if you like

Answer 3

which do you prefer?

Answer 4

well , i think using the product rule is easier

Answer 5

i can't seem to get it to look like the answer in the book though T__T

Answer 6

k
then \((fg)'=f'g+g'f\) with \(f(x)=x, f'(x)=1, g(x)=e^{-x}, g'(x)=-e^{-x}\) plug and chug then factor out the \(e^{-x}\) term

Answer 7

you get
\[e^{-x}-xe^{-x}\] as a first step

Answer 8

second step factor as\[e^{-x}(1-x)\]

Answer 9

ok now?

Answer 10

.

Answer 11

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

Answer 12

one of those 1s should be an \(x\)

Answer 13

can i ask why

Answer 14

look at the long post i wrote above that included the product rule

Answer 15

oh crap

Answer 16

you're so right thanks

Answer 17

kk yw

Answer 18

can i ask one more thing.. .. do u recommend quotient or product rule for this

Answer 19

which would you have done?

Answer 20

this one product, but not all

Answer 21

do it the other way and you will see why
but don't be scared of the quotient rule

Answer 22

ok thanks a lot satellite you are awesome =D

Answer 23

for example if you see something like
\[\frac{x+1}{x-1}\] the quotient rule is much much easier

Answer 24

i see i see

Answer 25

i have seen people try to rewrite it as \((x+1)(x-1)^{-1}\) and it becomes a big disater
thanks!

Answer 26

disaster too

Answer 27

lol