\begin{frame} \frametitle{Derivatives of Trigonometric Functions} \begin{block}{} \begin{malign} \frac{d}{dx} \sin x &= \cos x && \frac{d}{dx} \cos x = -\sin x \end{malign} \end{block} \medskip \begin{exampleblock}{} Differentiate $\tan x$: \begin{talign} \frac{d}{dx} \tan x &= \mpause[1]{ \frac{d}{dx} \left( \frac{\sin x}{\cos x} \right) } \\ &\mpause[2]{= \frac{\cos x \cdot \frac{d}{dx} \sin x - \sin x \cdot \frac{d}{dx}\cos x}{(\cos x)^2} } \\ &\mpause[3]{= \frac{\cos x \cdot \cos x - \sin x \cdot (-\sin x)}{\cos^2 x} } \\ &\mpause[4]{= \frac{\cos^2 x + \sin^2 x}{\cos^2 x} } \\ &\mpause[5]{= \frac{1}{\cos^2 x} } \mpause[6]{\;{\color{gray} = \sec^2 x}} \end{talign} \end{exampleblock} \vspace{10cm} \end{frame}