## Calculus: Early Transcendentals 8th Edition

$-\dfrac{y \sin xy}{x \sin xy+\cos y}$
Recall Equation 6: $\dfrac{dy}{dx}=-\dfrac{F_x}{F_y}$ ...(1) Given: $\cos x=1+\sin y$ Consider that $F(x,y)=\cos (xy)=1-\sin y=0$ $F_x=-y \sin xy\\F_y= -x \sin (xy) -\cos y$ Equation (1) becomes: $\dfrac{dy}{dx}=-\dfrac{-y \sin xy}{-x \sin (xy) -\cos y}=-\dfrac{y \sin xy}{x \sin xy+\cos y}$