\begin{frame}
  \frametitle{Differentiation Rules: Quotient Rule}

  \begin{block}{}
    \begin{malign}
      \left(\frac{f}{g}\right)'(x) \;=\; \frac{g(x) \cdot f'(x) - f(x) \cdot g'(x)}{g(x)^2}
    \end{malign}
  \end{block}
  \smallskip
  
  \begin{exampleblock}{}
    Find an equation to the tangent line to
    \begin{talign}
      f(x) = \frac{e^x}{1+x^2}
    \end{talign}
    at point $(1,\frac{e}{2})$. \pause
    We have
    \begin{talign}
      f'(x)
      &\mpause[1]{= \frac{(1+x^2)\cdot \frac{d}{dx}(e^x) - e^x \frac{d}{dx}(1+x^2)}{(1+x^2)^2} }  
      \mpause[2]{= \frac{(1+x^2)e^x - e^x \cdot 2x}{(1+x^2)^2} }  \\
      &\mpause[3]{= \frac{x^2 e^x - 2xe^x + e^x}{(1+x^2)^2} }  
      \mpause[4]{= \frac{(x - 1)^2 e^x}{(1+x^2)^2} }  
    \end{talign}
    \pause\pause\pause\pause\pause
    Thus the slope of the tangent is $f'(1) = 0$. \pause Hence the tangent is
    \begin{talign}
      y = \frac{e}{2}
    \end{talign}
  \end{exampleblock}  
  \vspace{10cm}
\end{frame}