\begin{frame}
  \frametitle{2nd Midterm Exam - Review}
  
  \begin{exampleblock}{}
    Use logarithmic differentiation to find the derivative of
    \begin{talign}
      y = \sqrt{\frac{x-1}{x^4 + 1}}
    \end{talign}\vspace{-2.5ex}
    \pause
    
    We have:
    \begin{talign}
      \ln y &= \ln \sqrt{\frac{x-1}{x^4 + 1}} 
            \mpause[1]{= \frac{1}{2}\cdot \ln \frac{x-1}{x^4 + 1}} 
            \mpause[2]{= \frac{1}{2}\cdot \left(\ln (x-1) - \ln (x^4 + 1)\right)} 
    \end{talign}
    \pause\pause\pause
    Thus
    \begin{talign}
      &\frac{d}{dx} \ln y = \frac{d}{dx} \left[ \frac{1}{2}\cdot \left(\ln (x-1) - \ln (x^4 + 1)\right) \right] \\
      &\mpause[1]{ \frac{1}{y}y' = \frac{1}{2}\cdot \left(\frac{d}{dx}\ln (x-1) - \frac{d}{dx}\ln (x^4 + 1)\right) }\\
      &\mpause[2]{ y' = \frac{1}{2}y\cdot \left(\frac{1}{x-1} - \frac{1}{x^4 + 1}{4x^3}\right) }\\
      &\mpause[3]{ y' = \frac{1}{2}\cdot \sqrt{\frac{x-1}{x^4 + 1}}\cdot \left(\frac{1}{x-1} - \frac{1}{x^4 + 1}{4x^3}\right) }
    \end{talign}
        
  \end{exampleblock}
\end{frame}