\begin{frame} \frametitle{Implicit Differentiation} \begin{block}{} We can use \emph{implicit differentiation}: \begin{itemize} \item differentiate both sides of the equation w.r.t. $x$, and \item then solve for $y'$, that is, for $\frac{dy}{dx}$ \end{itemize} \end{block} \begin{exampleblock}{} We differentiate $x^2 + y^2 = 25$ implicitly. We have \begin{talign} \frac{dy}{dx} = -\frac{x}{y} \end{talign} \pause Find an equation of the tangent at point $(3,4)$. \pause\medskip At point $(3,4)$ we have: \begin{talign} \frac{dy}{dx} = -\frac{3}{4} \end{talign} \pause Thus the tangent is \begin{talign} y - 4 = -\frac{3}{4} (x-3) \end{talign} \end{exampleblock} \vspace{10cm} \end{frame}