If cos (x+y)=y sin x then find `dx/dy`

Explanation

cos(x+y)= y sin x Differentiate both sides with respect to x
`-sin (x+y) d/dx(x+y)=y.cos x+sin x dy/dx`
`rArr -sin (x+y)[1+dy/dx]=y.cos x+sin xdy/dx`
`rArr -sin(x+y)-sinx.dx/dy`
`rArr -sin (x+y)[1+dy/dx]=y.cos x+sin xdy/dx`
`rArr -sin(x+y)-sinx.dy/dx=cos x+sin x. dy/dx`
`rArr -dy/dx[sin (x+y)+sin x]=ycosx+sin (x+y)`
`rArr dy/dx =-(y cos c +sin (x+y))/(sin (x+y)+sin x)`