\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 &= \ln (x+1) - \ln \sqrt{x-2} \\ &\mpause[1]{ = \ln (x+1) - \frac{1}{2} \ln (x-2)} \end{talign} \pause\pause Thus \begin{talign} y' &= \frac{1}{x+1} - \frac{1}{2} \cdot \frac{1}{x-2} \end{talign} \end{exampleblock} \vspace{10cm} \end{frame}