Question

Find dy/dx for the implicit function: xy+x=e^y

Answer 1

Have you started the problem?

Answer 2

To do these you just treat 'y' as some unknown function of x...

Answer 3

i dont know how to differentiate e^y...

Answer 4

so for example, differentiating 'y' : d/dx (y) gives you y'

differentiating some function of y, like say, y^2 you use the chain rule:
d/dx (y^2) = 2*y*y'

Answer 5

ah ok so the rule for e^f(x) is (e^f(x)) ' = e^f(x) * f '(x)

Answer 6

so it's e^y * y'

Answer 7

\[(e ^{y})\prime = e ^{y} *y \prime \]

Answer 8

is it
x(dy/dx) + y + 1 = (dy/dx)(e^y)
dy/dx = -(y+1)/(x-e^y) ??

Answer 9

yes

Answer 10

thanks!

Answer 11

give @Algebraic! a medal please

Answer 12

you're welcome

Answer 13

rfl

Answer 14

how can i give a medal?? i am new here

Answer 15

press best response button next to one of his responses

Answer 16

\[xy+x=e^y\]
\[\frac{\text d}{\text dx}(xy+x)=\frac{\text d}{\text dx}e^y\]

\[y+x\frac{\text dy}{\text dx}+1=\frac{\text dy}{\text dx}e^y\]

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

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

Answer 17

pretty

Answer 18

i wish someone did that to my replies....

Answer 19

what do you mean?

Answer 20

i meant what @EulerGroupie did. he told you to give @Algebraic! a medal...no one ever tells people to give @lgbasallote a medal...

Answer 21

:(

Answer 22

:*(

Answer 23

dere u go XD

Answer 24

lol i didn't say no one gives me medals. i said no one tells others to give me medals