Find `(dy)/(dx)` if `y+siny=cosx`

Explanation

`y+siny=cosx` Differentiating throughout w.r.y.x we get `(dy)/(dx)+cosy(dy)/(dx)=-sinx(dy)/(dx)(1+cosy)=-sinx(dy)/(dx)=(-sinx)/(1+cosy)` where `cosyne-1`