# Differentiation rules I

Math Modeling in the News – Hurricane Sandy

Learning objectives

• Compute derivatives of the basic modeling functions: $t^N$, $e^{kt}$, polynomials, $\ln t$
• Compute derivatives of linear combinations: $af(t) + bg(t)$
• Use the chain rule for the derivative of a function $f(g(t))$
• Use the product rule for the derivative of a function $f(t)g(t)$
• Use algebraic differentiation to answer questions in applied contexts
• Explore Wolfram Alpha

Before class

• Read Hughes-Hallett 3.1, 3.2, 3.3, 3.4 (product rule only).
• Ponder problems 3.1. 2, 6, 8, 20, 30, 38, 46, 48, 52, 60; 3.2. 2, 12,16, 26, 34, 40, 44; 3.3. 2, 4, 6,12,14, 42; 3.4. 6, 8, 27, 35, 37.
• Study the formula sheet

In class