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 \(\displaystyle y=\sqrt{\tan^{-1}(4x^{3})},\) what is \(\displaystyle \frac{dy}{dx}?\)

Given \(\displaystyle e^{xy}=\sin (2x+7y),\) what is \(\displaystyle \frac{dy}{dx}?\)

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