\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 \begin{talign} y = \sqrt{\ln x} \end{talign} \pause We have \begin{talign} y' = \frac{1}{2\sqrt{\ln x}} \cdot \frac{1}{x} \end{talign} \end{exampleblock} \pause \begin{exampleblock}{} Differentiate \begin{talign} y = \log_{10}(2+\sin x) \end{talign} \pause We have \begin{talign} y' = \frac{1}{(2+\sin x)\ln 10} \cdot \cos x \end{talign} \end{exampleblock} \vspace{10cm} \end{frame}