\begin{frame} \frametitle{Differentiation Rules: Quotient Rule} \begin{block}{} \begin{malign} \left(\frac{f}{g}\right)'(x) \;=\; \frac{g(x) \cdot f'(x) - f(x) \cdot g'(x)}{g(x)^2} \end{malign} \end{block} \pause\smallskip \begin{exampleblock}{} Let \vspace{-1ex} \begin{talign} f(x) = \frac{x^2 + x - 2}{x^3 + 6} \end{talign} Then \begin{talign} f'(x) &\mpause[1]{= \frac{(x^3 + 6) \cdot \frac{d}{dx}(x^2 + x - 2) - (x^2 + x - 2) \cdot \frac{d}{dx}(x^3 + 6)}{(x^3 + 6)^2}} \\ &\mpause[2]{= \frac{(x^3 + 6) \cdot (2x + 1) - (x^2 + x - 2) \cdot 3x^2}{(x^3 + 6)^2}} \\ &\mpause[3]{= \frac{(2x^4 + x^3 + 12x + 6) - (3x^4 + 3x^3 - 6x^2)}{(x^3 + 6)^2}} \\ &\mpause[4]{= \frac{-x^4 - 2x^3 + 6x^2 + 12x + 6}{(x^3 + 6)^2}} \end{talign} \end{exampleblock} \vspace{10cm} \end{frame}