Symbolic differentiation

Learning objectives

  • Compute derivatives of the basic modeling functions: t^N, polynomials, e^{kt}, \cos kt, \sin kt,  \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)
  • Find the equation of a tangent line:  y=f(a) + f^\prime(a)\, \Delta x where y=f(x) and \Delta x = x-a
  • Use algebraic differentiation to answer questions in applied contexts

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
  • Study reasons for the formulas

In class