Answer
$-\dfrac{y \sin xy}{x \sin xy+\cos y}$
Work Step by Step
We are given that $ \cos x=1+\sin y$
$F(x,y)=\cos (xy)=1-\sin y=0$
$F_x=-y \sin xy$ and $F_y= -x \sin (xy) -\cos y$
Use Equation 6 which is: $\dfrac{dy}{dx}=-\dfrac{F_x}{F_y}$
This implies that
$\dfrac{dy}{dx}=-\dfrac{-y \sin xy}{-x \sin (xy) -\cos y}=-\dfrac{y \sin xy}{x \sin xy+\cos y}$
