Help finding the derivative of (e^xy)

[CeceBear]

Homework Statement

y= e^xy
y'= ?

Homework Equations

y' [a^x] = lna(a^x)
y' [uv] = uv' + vu'

The Attempt at a Solution

y = e^xy
lny = lne^xy
lny = xy(lne) = xy
(1/y)y' = (x)(y') + (y)(1)
y' = xy(y') + y^2

From here I don't know how to isolate the derivative. (And I feel like I shouldn't have done this implicitly...)

 

[eumyang]

Homework Statement

y= e^xy
y'= ?

Homework Equations

y' [a^x] = lna(a^x)
y' [uv] = uv' + vu'

The Attempt at a Solution

y = e^xy
lny = lne^xy
lny = xy(lne) = xy
(1/y)y' = (x)(y') + (y)(1)
y' = xy(y') + y^2

From here I don't know how to isolate the derivative. (And I feel like I shouldn't have done this implicitly...)

Looks like you're fine so far. Now move the xy(y') term to the left-hand side and factor out the y'. Can you go on from there?