\begin{frame} \frametitle{2nd Midterm Exam - Review} \begin{exampleblock}{} Find the derivative of \begin{align*} f(x) = \frac{\sqrt{x}-2}{\sqrt{x}+2} \end{align*} using the quotient rule. \pause\medskip \begin{align*} f'(x) &= \mpause[1]{ \frac{(\sqrt{x}+2) \frac{d}{dx}(\sqrt{x}-2) - (\sqrt{x}-2) \frac{d}{dx}(\sqrt{x}+2) }{(\sqrt{x}+2)^2} } \\ &\mpause[2]{= \frac{(\sqrt{x}+2) \frac{1}{2\sqrt{x}} - (\sqrt{x}-2) \frac{1}{2\sqrt{x}} }{(\sqrt{x}+2)^2} } \\ &\mpause[3]{= \frac{(\sqrt{x}+2) - (\sqrt{x}-2) }{2\sqrt{x} (\sqrt{x}+2)^2} } \\ &\mpause[4]{= \frac{4}{2\sqrt{x} (\sqrt{x}+2)^2} } \mpause[5]{= \frac{2}{\sqrt{x} (\sqrt{x}+2)^2} } \end{align*} \end{exampleblock} \end{frame}