\begin{frame} \frametitle{2nd Midterm Exam - Review} \begin{exampleblock}{} Find the derivative of \begin{align*} f(x) = \frac{\sqrt{x^3}+4}{3x^2+7} \end{align*} using the quotient rule. \pause\medskip \begin{align*} f'(x) &= \mpause[1]{ \frac{(3x^2+7) \cdot \frac{d}{dx}(\sqrt{x^3}+4) - (\sqrt{x^3}+4) \cdot \frac{d}{dx} (3x^2+7)}{(3x^2+7)^2} } \\ &\mpause[2]{= \frac{(3x^2+7) \cdot \frac{d}{dx}(x^{\frac{3}{2}}+4) - (\sqrt{x^3}+4) \cdot \frac{d}{dx} (3x^2+7)}{(3x^2+7)^2} } \\ &\mpause[3]{= \frac{(3x^2+7) \cdot \frac{3}{2}\cdot x^{\frac{1}{2}} - (\sqrt{x^3}+4) \cdot 6x}{(3x^2+7)^2} } \end{align*} \end{exampleblock} \end{frame}