`y = sin(xy)` Find `dy/dx` by implicit differentiation.

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`y=sin(xy)`

Differentiating both sides with respect to x,

`dy/dx=cos(xy) d/(dx)(xy)`

`dy/dx=cos(xy)*(xdy/dx+y)`

`dy/dx=xcos(xy)dy/dx+ycos(xy)`

`dy/dx-xcos(xy)dy/dx=ycos(xy)`

`dy/(dx)(1-xcos(xy))=ycos(xy)`

`dy/dx=(ycos(xy))/(1-xcos(xy))`

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`y=sin(xy)`

Differentiating both sides with respect to x,

`dy/dx=cos(xy) d/(dx)(xy)`

`dy/dx=cos(xy)*(xdy/dx+y)`

`dy/dx=xcos(xy)dy/dx+ycos(xy)`

`dy/dx-xcos(xy)dy/dx=ycos(xy)`

`dy/(dx)(1-xcos(xy))=ycos(xy)`

`dy/dx=(ycos(xy))/(1-xcos(xy))`

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