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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 \(\sqrt[3]{x^2}+\sqrt[3]{y^2}=4,\) what is \(\displaystyle \frac{dy}{dx}?\)

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If \(x=y\sqrt{11+y}\), what is \(\displaystyle \frac{dy}{dx}?\)

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Find \(\displaystyle \frac{dy}{dx}\) for \(7\sqrt{x}+6\sqrt{y}=13y^2\) at the point \((1,1).\)

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Given \[f(x)=\sqrt[3]{\frac{x}{x^2+124}},\] what is the value of \(f'(1)?\)

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If \(\sqrt{3x}+\sqrt{y}=\sqrt{5}\), what is \(\displaystyle \frac{dy}{dx}?\)

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