\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}