Calculus
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 \(\displaystyle \frac{dy}{dx}?\)
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 \((x,y) = (0,1) \).