\begin{frame} \frametitle{Differentiation Rules: Quotient Rule} \begin{block}{Quotient Rule} If $f$ and $g$ are both differentiable, then \begin{talign} \frac{d}{dx} \left[\frac{f(x)}{g(x)}\right] \;=\; \frac{ g(x) \cdot \frac{d}{dx}( f(x) ) - f(x) \cdot \frac{d}{dx}( g(x) ) }{[g(x)]^2} \end{talign} \end{block} \pause\medskip In different notation \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\medskip In words: \begin{itemize} \item [] The derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. \end{itemize} \end{frame}