Implicit Differentiation

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

\frac{2xye^{x^2}-5x^{4}y^{6}}{10y^{9}+6x^{4}y^{4}-e^{x^2}}

\frac{2xye^{x^2}-5x^{3}y^{5}}{10y^{9}+6x^{4}y^{4}-e^{x^2}}

\frac{2xye^{x^2}-5x^{3}y^{5}}{10y^{9}+6x^{5}y^{5}-e^{x^2}}

\frac{2xye^{x^2}-5x^{4}y^{6}}{10y^{9}+6x^{5}y^{5}-e^{x^2}}

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 $(x,y) = (0,1)$ .

Implicit Differentiation - Exponential and Logarithmic Functions