Implicit Differentiation

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

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

\[\displaystyle{ \frac{dy}{dx}=\frac{y(6y+e^{x/y})}{4y^2-xe^{x/y}}} \] \[\displaystyle{ \frac{dy}{dx}=\frac{y(6y-e^{x/y})}{4y^2-xe^{x/y}}} \] \[\displaystyle{ \frac{dy}{dx}=\frac{y(4y-e^{x/y})}{6y^2-xe^{x/y}}} \] \[\displaystyle{ \frac{dy}{dx}=\frac{y(4y+e^{x/y})}{6y^2-xe^{x/y}}} \]

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

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

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

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Implicit Differentiation - Exponential and Logarithmic Functions

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