\begin{frame}
  \frametitle{Derivatives}
  
  \begin{block}{}
    The \emph{derivative of a function $f$ at a number $a$}, denoted $f'(a)$, is
    \begin{talign}
      f'(a) = \lim_{h\to 0} \frac{f(a+h) - f(a)}{h}
    \end{talign}
    if the limit exits.
  \end{block}
  \pause
  \begin{exampleblock}{}
    Find the derivative of $f(x) = x^2 - 8x + 9$ at number $a$.
    \pause
    \begin{talign}
      f'(a) 
      &= \lim_{h\to 0} \frac{f(a+h) - f(a)}{h}\\
      &\mpause[1]{= \lim_{h\to 0} \frac{[(a+h)^2 - 8(a+h) + 9] - [a^2 - 8a + 9]}{h}}\\
      &\mpause[2]{= \lim_{h\to 0} \frac{a^2+2ah+h^2 - 8a - 8h + 9 - a^2 + 8a - 9}{h}}\\
      &\mpause[3]{= \lim_{h\to 0} \frac{2ah + h^2 - 8h}{h}}
      \mpause[4]{= \lim_{h\to 0} (2a + h - 8)}\\
      &\mpause[5]{= 2a-8}
    \end{talign}
  \end{exampleblock}
  \vspace{15cm}
\end{frame}