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

  Lets $f$ and $g$ be linear functions:
  \begin{talign}
    f(x) = ax + b && g(x) = cx + d
  \end{talign}
  \pause
  \begin{exampleblock}{}
    What is the derivative of $f\cdot g$?
  \end{exampleblock}\vspace{-3ex}
  \pause
  \begin{talign}
    \alert<8->{(f\cdot g)'(x)} &= \frac{d}{dx} [f(x)\cdot g(x)]\\
    &\mpause[1]{= \frac{d}{dx} [(ax+b)\cdot (cx+d)] }\\
    &\mpause[2]{= \frac{d}{dx} [acx^2 + adx + bcx + bd] }\\
    &\mpause[3]{= 2acx + ad + bc} \\
    &\mpause[4]{= a(cx + d) + c(ax + b)} \\
    &\mpause[5]{= \alert{f'(x) \cdot g(x) + g'(x) \cdot f(x)}}
  \end{talign}
  \pause\pause\pause\pause\pause\pause
  We will now see that this also holds for general $f$ and $g$.
\end{frame}