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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 \(\displaystyle y^{10}+x^{5}y^{6}=2+ye^{x^2},\) what is \(\displaystyle \frac{dy}{dx}?\)

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If \(\displaystyle e^{\frac{x}{y}}=4x-6y,\) what is \(\displaystyle \frac{dy}{dx}?\)

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What is the equation of the tangent line to \(\ln (x+4y)+3e^y=3\) at the point \((1,0)?\)

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If \(y=(\ln x)^x\), what is the derivative of \(y\) at \(x=e\)?

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Given \(e^{2xy} = y^2\), what is the value of \(\frac{dy}{dx}\) at \((x,y) = (0,1) \).

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