\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}
  \pause\smallskip
  
  \begin{exampleblock}{}
    Let \vspace{-1ex}
    \begin{talign}
      f(x) = \frac{x^2 + x - 2}{x^3 + 6}
    \end{talign}
    Then
    \begin{talign}
      f'(x) 
      &\mpause[1]{= \frac{(x^3 + 6) \cdot \frac{d}{dx}(x^2 + x - 2) - (x^2 + x - 2) \cdot \frac{d}{dx}(x^3 + 6)}{(x^3 + 6)^2}}  \\
      &\mpause[2]{= \frac{(x^3 + 6) \cdot (2x + 1) - (x^2 + x - 2) \cdot 3x^2}{(x^3 + 6)^2}}  \\
      &\mpause[3]{= \frac{(2x^4 + x^3 + 12x + 6) - (3x^4 + 3x^3 - 6x^2)}{(x^3 + 6)^2}}  \\
      &\mpause[4]{= \frac{-x^4 - 2x^3 + 6x^2 + 12x + 6}{(x^3 + 6)^2}}  
    \end{talign}
  \end{exampleblock}  
  \vspace{10cm}
\end{frame}