\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}