Answer:
[tex]\frac{dy}{dx}=\frac{-y\sin xy}{1+\sin xy}[/tex]
Step-by-step explanation:
[tex]\frac{dy}{dx}=-\frac{d}{dx} (xy) \sin(xy) \\ \\ =-\left(x \frac{dy}{dx}+y \right) \sin(xy) \\ \\ =-x \frac{dy}{dx} \sin(xy)-y\sin(xy) \\ \\ \frac{dy}{dx}(1+x\sin(xy))=-y \sin xy \\ \\ \frac{dy}{dx}=\frac{-y\sin xy}{1+\sin xy}[/tex]
