Question

Find dy/dx of ln(xy) = e^(x+y)

Answer 1

Take derivative both sides

Answer 2

solve for dy/dx,

Answer 3

y'/(xy) = e^(x+y)*(1-y') ? Is this correct

Answer 4

(1+y')*****

Answer 5

yes

Answer 6

Apparently I'm making a dumb error solving for y' then :(

Answer 7

\(\dfrac{y'}{xy}=e^{x+y}(1+y')=e^{x+y}+e^{x+y}y'\)

Answer 8

\(y'=xy(e^{x+y}+e^{x+y}y')= xye^{x+y}+xye^{x+y}y'\)

Answer 9

Move y' to the same side
\(y'-xye^{x+y}y'=xye^{x+y}\)
factor y'

Answer 10

@tjb69812

Answer 11

\(y' (1-xye^{x+y})=xye^{x+y}\)

Answer 12

isolate y'

Answer 13

\(\dfrac{dy}{dx}= \dfrac{xye^{x+y}}{1-xye^{x+y}}\)

Answer 14

ok?

Answer 15

Yes! Thanks a ton

Answer 16

yw