If \(\sin(xy)=x\), then \(\dfrac{dy}{dx}=\)

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$$ \sin(xy)=x $$ $$ \cos(xy)\cdot \left(x\frac{dy}{dx}+y\right)=1 $$ $$ x\frac{dy}{dx}+y = \frac{1}{\cos(xy)} $$ $$ x\frac{dy}{dx}= \frac{1}{\cos(xy)} -y $$ $$ x\frac{dy}{dx}= \frac{1-y\cos(xy)}{\cos(xy)} $$ $$ \frac{dy}{dx}=\boxed{\frac{1-y\cos(xy)}{x\cos(xy)} } $$