Calculus

# Implicit Differentiation - Exponential and 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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