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\begin{frame}
  \frametitle{Derivatives of Logarithmic Functions}

  \begin{block}{}
    \begin{malign}
      \frac{d}{dx} (\log_a x) = \frac{1}{x\ln a}
      &&
      \frac{d}{dx} (\ln x) = \frac{1}{x}
    \end{malign}
  \end{block}

  \begin{exampleblock}{}
    Differentiate\vspace{-1ex}
    \begin{talign}
      y = \ln \frac{x+1}{\sqrt{x-2}} 
    \end{talign}\vspace{-2ex}%
    
    \pause
    We have 
    \begin{talign}
      y' 
      &= \mpause[1]{ \frac{1}{\frac{x+1}{\sqrt{x-2}}} \cdot \frac{d}{dx} \frac{x+1}{\sqrt{x-2}}} \\
      &\mpause[2]{= \frac{\sqrt{x-2}}{x+1} \cdot \frac{1\cdot \sqrt{x-2} - (x+1) \cdot \frac{d}{dx} \sqrt{x-2}}{(\sqrt{x-2})^2}} \\
      &\mpause[3]{= \frac{\sqrt{x-2}}{x+1} \cdot \frac{\sqrt{x-2} - (x+1) \cdot \frac{1}{2\sqrt{x-2}}\cdot 1}{(\sqrt{x-2})^2}} \\
      &\mpause[4]{= \frac{x-2 - (x+1) \cdot \frac{1}{2}}{(x+1)(x-2)}} 
      \mpause[5]{= \frac{x-5}{2(x+1)(x-2)}} 
    \end{talign}
  \end{exampleblock}
  \vspace{10cm}  
\end{frame}