We can rearrange and simplify to get:
-2xsin(x-y)=y
d/dx[y]=d/dx[-2xsin(x-y)]
d/dx[y]=d/dx[-2x]sin(x-y)-2xd/dx[sin(x-y)]
d/dx[y]=-2sin(x-y)-2xd/dx[sin(x-y)]
d/dx[y]=-2sin(x-y)-2xcos(x-y)d/dx[x-y]
d/dx[y]=-2sin(x-y)-2xcos(x-y)(d/dx[x]-d/dx[y])
d/dx[y]=-2sin(x-y)-2xcos(x-y)(d/dx[x]-d/dx[y])
Using the chqain rule we get that d/dx=dy/dx*d/dy
dy/dxd/dy[y]=-2sin(x-y)-2xcos(x-y)(1-dy/dxd/dy[y])
dy/dx=-2sin(x-y)-2xcos(x-y)(1-dy/dx)
dy/dx=-2sin(x-y)-2xcos(x-y)+2xcos(x-y)dy/dx
dy/dx-2xcos(x-y)dy/dx=-2sin(x-y)-2xcos(x-y)
dy/dx[1-2xcos(x-y)]=-2sin(x-y)-2xcos(x-y)
dy/dx=-(2sin(x-y)+2xcos(x-y))/(1-2xcos(x-y))