\begin{frame}
  \frametitle{Derivative: Other Notations}
  
  We usually write $f'(x)$ for the derivative. 
  \pause\bigskip
  
  However, there are other common notations:
  \begin{talign}
    f'(x) \mpause[1]{= y'} \mpause[2]{= \frac{dy}{dx}} \mpause[3]{= \frac{df}{dx}} 
    \mpause[4]{= \frac{d}{dx}f(x)} \mpause[5]{= Df(x)} \mpause[6]{= D_x f(x)}  
  \end{talign}%
  \pause[9]%
  The symbols $\frac{d}{dx}$ and $D$ are called \emph{differentiation operators}.\\
  (they indicate the operation of computing the derivative)
  \pause\bigskip
  
  The notation $\frac{dy}{dx}$ has been introduced by Leibnitz:
  \begin{talign}
    \frac{dy}{dx} = \lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}
  \end{talign}
  \pause
  
  In Leibnitz notation $f'(a)$ is written as
  \begin{talign}
    \left. \frac{dy}{dx} \right|_{a} &&\text{ or} && \left. \frac{dy}{dx} \right]_{a}
  \end{talign}
\end{frame}