Please help me differentiate

PLEASE NOTE :  I have no idea if this is correct - someone please check   

sin(x+y)=cosy

differentiate y in terms of x

$$\begin{array}{rll} sin(x+y)&=&cosy\\\\ cos(x+y)[1+\frac{dy}{dx}]&=&-(siny)\frac{dy}{dx}\\\\ cos(x+y)+cos(x+y)\frac{dy}{dx}+(siny)\frac{dy}{dx}&=&0\\\\ cos(x+y)\frac{dy}{dx}+(siny)\frac{dy}{dx}&=&-cos(x+y)\\\\ \frac{dy}{dx}[cos(x+y)+(siny)]&=&-cos(x+y)\\\\ \frac{dy}{dx}&=&\frac{-cos(x+y)}{cos(x+y)+(siny)}\\\\ \end{array}$$

If that is correct then i guess

$$\frac{dx}{dy}&=&\frac{cos(x+y)+(siny)}{-cos(x+y)}\\\\$$

Both answers are correct, Melody....

Thanks Chris.   

Ahh, thanks guys!