\begin{frame} \frametitle{2nd Midterm Exam - Review} \begin{exampleblock}{} Find the derivative of \begin{align*} f(x) = \left(\frac{1}{x^3} - 3\frac{1}{x}\right)\cdot (2x^4+ 5x) \end{align*} using the product rule. \pause \begin{align*} &f'(x) = \mpause[1]{ \left(\frac{1}{x^3} - 3\frac{1}{x}\right) \cdot \frac{d}{dx} (2x^4+ 5x) + (2x^4+ 5x) \frac{d}{dx} \left(\frac{1}{x^3} - 3\frac{1}{x}\right) } \\ &\mpause[2]{= \left(\frac{1}{x^3} - 3\frac{1}{x}\right) \cdot (8x^3+ 5) + (2x^4+ 5x) \left(-3x^{-4} - 3\cdot (-1)x^{-2}\right) } \\ &\mpause[3]{= \left(\frac{1}{x^3} - 3\frac{1}{x}\right) \cdot (8x^3+ 5) + (2x^4+ 5x) \left(\frac{-3}{x^{4}} + \frac{3}{x^{2}}\right) } \\ &\mpause[4]{= \left(8 - 24x^2 + \frac{5}{x^3} - \frac{15}{x}\right) + \left(-6 + 6x^2 - \frac{15}{x^3} + \frac{15}{x} \right) } \\ &\mpause[5]{= 2 - 18x^2 - \frac{10}{x^3} } \end{align*} \end{exampleblock} \end{frame}