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

  \begin{block}{}
    \begin{malign}
      (f\circ g)'(x) \;=\; f'(g(x)) \cdot g'(x)
    \end{malign}
  \end{block}  

  \begin{exampleblock}{}
    Differentiate $f(x) = (x^3-1)^{100}$.
    \pause\medskip
    
    We have that
    \begin{talign}
      f(x) &= g(h(x)) &\text{where}&&
      g(x) &= \mpause[1]{x^{100}} &
      h(x) &= \mpause[1]{x^3-1}
    \end{talign}
    \pause\pause
    and
    \begin{talign}
      g'(x) = \mpause[1]{100x^{99}} &&
      h'(x) = \mpause[2]{3x^2}
    \end{talign}
    \pause\pause\pause
    
    Hence:
    \begin{talign}
      f'(x) = (g\circ h)'(x) &= 
      \mpause[1]{ 100(x^3-1)^{99} \cdot 3x^2 } \\
      &\mpause[2]{= 300x^2\cdot (x^3-1)^{99}  }
    \end{talign}
  \end{exampleblock}
  \vspace{10cm}
\end{frame}