Question

find the derivative of e^(x+y) = x+y

Answer 1

wrt \(x\)?

Answer 2

what is wrt?

Answer 3

with respect to \(x\) in other words are you looking for \(\frac{dy}{dx}\) ?

Answer 4

yes

Answer 5

actually no

Answer 6

the question says find Dy (with a tiny x in the middle)

Answer 7

looks like an implicit differentiation problem ...yes?

Answer 8

yes

Answer 9

derivative of the right hand side is \(1+y'\) the derivative of the left is
\[(1+y')e^{x+y}\]

Answer 10

set them equal, solve for \(y'\)

Answer 11

but won't the y' cancel out?

Answer 12

no i don't think so

Answer 13

wouldnt you end up with e^(x+y) = (1+y')/(1+y')?

Answer 14

sorry, this is where i got stuck

Answer 15

\[(1+y')e^{x+y}=1+y'\]
\[e^{x+y}+y'e^{x+y}=1+y'\]
\[y'e^{x+y}-y'=1-e^{x+y}\] etc etc

Answer 16

oh ok we can finish, but i hope it is clear that it is algebra all the way

Answer 17

that makes so much more sense....

Answer 18

\[y'(e^{x+y}-1)=1-e^{x+y}\]
\[y'=\frac{1-e^{x+y}}{e^{x+y}-1}\]
\[y'=-1\]

Answer 19

wait i dont get how its -1

Answer 20

check my algebra, but in general
\[\frac{a-b}{b-a}=-1\]

Answer 21

ah ok, thank you satellite73 :)

Answer 22

yw