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Not all equations can be written like y = f(x), so taking the derivative can be tricky. Save the mess and do it directly with implicit differentiation.

If \(10xy=\cot(xy),\) what is \(\displaystyle \frac{dy}{dx}?\)

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If \(7\cos x \sin y=11,\) what is \(\displaystyle \frac{dy}{dx}?\)

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If \(\sin (x+3y)=y^{4}\cos x,\) what is \(\frac{dy}{dx}?\)

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If \(x^2y^2+x\sin y=13,\) what is \(\displaystyle \frac{dy}{dx}?\)

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