\begin{frame}
  \frametitle{Derivatives of Basic Functions}
  
  \begin{block}{Sum Rule}
    If $f$ and $g$ are differentiable, then
    \begin{talign}
      \frac{d}{dx}[f(x) + g(x)] \;=\; \frac{d}{dx}f(x) + \frac{d}{dx}g(x)
    \end{talign}
  \end{block}
  \pause
  
  \begin{proof}
    \begin{malign}
    \frac{d}{dx}[f(x) + g(x)] 
    &\mpause[1]{ = \lim_{h\to 0} \frac{[f(x+h) + g(x+h)] - [f(x) + g(x)]}{h} } \\
    &\mpause[2]{ = \lim_{h\to 0} \frac{[f(x+h) - f(x)] + [g(x+h) - g(x)]}{h} } \\
    &\mpause[3]{ = \lim_{h\to 0} \left( \frac{f(x+h) - f(x)}{h} + \frac{g(x+h) - g(x)}{h} \right) } \\
    &\mpause[4]{ = \lim_{h\to 0} \frac{f(x+h) - f(x)}{h} + \lim_{h\to 0} \frac{g(x+h) - g(x)}{h}  } \\
    &\mpause[5]{ =  \frac{d}{dx}f(x) + \frac{d}{dx}g(x) }
    \end{malign}
  \end{proof}
\end{frame}