\begin{frame}
  \frametitle{Higher Derivatives}

  We can continue this process of deriving:
  \begin{itemize}
  \pause
    \item $f'''(x) = (f'')'(x)$
  \pause
    \item $f''''(x) = (f''')'(x)$
  \pause
    \item \ldots
  \end{itemize}
  
  \pause
  \begin{exampleblock}{}
    The $n$-th derivative of $f$ is denoted by 
    \begin{talign}
      f^{(n)}(x) &&\text{or}&& \frac{d^ny}{dx^n}
    \end{talign}
  \end{exampleblock}
  \pause
  For example,\quad $f = f^{(0)}$,\quad $f' = f^{(1)}$,\quad $f'' = f^{(2)}$,\quad $f''' = f^{(3)}$
  \pause\medskip
  
  \begin{exampleblock}{}
    Let $f(x) = x^3 - x$. Find $f'''(x)$ and $f^{(4)}(x)$.
    \pause\medskip
    
    We know $f''(x) = 6x$. \pause Hence
    \begin{talign}
      f'''(x) = \mpause[1]{6} && \mpause[2]{f^{(4)}(x) = \mpause[3]{0}}
    \end{talign}
    \pause\pause\pause\pause
    Note that $f'''$ is the slope of $f''$, and $f^{(4)}$ is the slope of $f'''$.
  \end{exampleblock}
\end{frame}