\begin{frame} \frametitle{Derivatives of Exponential Functions} \begin{block}{} \begin{malign} \frac{d}{dx}(e^x) \;=\; e^x \end{malign} \end{block} \pause\medskip \begin{block}{} \begin{malign} \frac{d}{dx}(a^x) \;=\; \ln a \cdot a^x \end{malign} \end{block} \pause\medskip \begin{exampleblock}{} At what point on the curve $e^x$ is the tangent parallel to $y = 2x$? \pause\medskip Let $f(x) = e^x$ \begin{talign} f'(a) = e^a = 2 \end{talign} \pause Thus $a = \ln 2$, that is, the point is $(a,e^a) = (\ln 2, 2)$. \end{exampleblock} \end{frame}