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## Implicit Differentiation

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.

# Exponential/Logarithmic Functions

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 $$\displaystyle \frac{dy}{dx}?$$

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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