I'm not sure what the value of the power is. But I'll solve it the way I think it's written.
y = xe^(-sinx) - ycosx
y' = (x)[-cosx * e^(-sinx)] + e^(-sinx) - [(y)(-sinx) + cosx]
= -x*cosx*e^(-sinx) + e^(-sinx) + y*sinx - cosx
This is technically the answer, but it could be simplified further, which will result as the following:
y' = [e^(-sinx)](x*cosx + 1) + y*sinx - cosx
