What is the Implicit Differentiation Equation for eysinx=x+xy?

[UsernameValid]

Equation: e^ysinx=x+xy

I took the derivative of both sides.
For the side with e^ysinx, I used the product rule and chain rule to get: e^y*cosx + e^y*sinx*y'
For the side with x+xy, I used the sum and product rule to get 1+y+xy'

So my resulting equation is: e^y*cosx + e^y*sinx*y'=1+y+xy', which I don't know how to solve and is probably wrong.

 

[HallsofIvy]

Why would you not knowhow to solve that for y'? If the problem were A+ By'= C+ Dy', could you solve for y'?

 

[ldm]

express y' as a function of x and y