\begin{frame} \frametitle{Derivatives of Basic Functions} \begin{block}{} The derivative of a constant function \begin{talign} \frac{d}{dx}(c) \;=\; 0 \end{talign} \end{block} \pause\smallskip \begin{block}{} \begin{malign} \frac{d}{dx}(x) \;=\; 1 \end{malign} \end{block} \pause\smallskip \begin{block}{} If $n$ is any real number, then \begin{talign} \frac{d}{dx}(x^n) \;=\; n\, x^{n-1} \end{talign} \end{block} \pause\smallskip \begin{exampleblock}{} Differentiate the following functions: \begin{itemize} \pause \item $\frac{d}{dx}(x^7) \;\;=\;\; \pause 7x^{6}$ \pause\smallskip \item $\frac{d}{dx}(\frac{1}{x^2}) \;\;=\;\; \pause \frac{d}{dx}(x^{-2}) \;\;=\;\; \pause -2\,x^{-3} \pause\;\;=\;\; -\frac{2}{x^{3}}$ \pause\smallskip \item $\frac{d}{dx}(\sqrt[3]{x^2}) \;\;=\;\; \pause \frac{d}{dx}(x^{\frac{2}{3}}) \;\;=\;\; \pause \frac{2}{3}\,x^{\frac{2}{3}-1} \;\;=\;\; \frac{2}{3}\,x^{-\frac{1}{3}}$ \end{itemize} \end{exampleblock} \vspace{10cm} \end{frame}