\begin{frame} \frametitle{Implicit Differentiation} \begin{exampleblock}{} Find $y'$ where $x^3 + y^3 = 6xy$. \begin{talign} y' = \frac{ 2y - x^2}{y^2 - 2x} \end{talign} Find the tangent to the curve at point $(3,3)$:\pause \begin{talign} y' = \frac{ 2\cdot 3 - 3^2}{3^2 - 2\cdot 3} = -1 \end{talign} \pause Thus the tangent is \quad $y - 3 = -1(x - 3)$. \end{exampleblock} \vspace{10cm} \end{frame}