Answer
$\dfrac{dy}{dx}=\dfrac{y\cos{xy}}{1-x\cos{xy}}.$
Work Step by Step
$\dfrac{d}{dx}(y)=\dfrac{d}{dx}(\sin{xy})\rightarrow$
Using the Chain Rule with $u=xy\rightarrow \dfrac{du}{dx}=y+x\dfrac{dy}{dx}\rightarrow$
$\dfrac{d}{dx}(\sin{xy})=(y+x\dfrac{dy}{dx})\cos{xy}\rightarrow$
$\dfrac{dy}{dx}=(y+x\dfrac{dy}{dx})\cos{xy}\rightarrow$
$\dfrac{dy}{dx}(1-x\cos{xy})=y\cos{xy}\rightarrow$
$\dfrac{dy}{dx}=\dfrac{y\cos{xy}}{1-x\cos{xy}}.$
