DERIVATIVES

DERIVATIVES

1. Rules for differentiation

   • Positive Integer Powers, Multiples, Sums and Differences
   • Products and Quotients
   • Negative Integer Powers of x
   • Second and Higher Order Derivatives

2. Velocity and Other Rates of Change

   • Instantaneous Rates of Change
   • Motion Along a Line
   • Sensitivity to Change
   • Derivatives in Economics

3. Derivative of a Function

   • Definition Of Derivatives
   • Notation
   • Relationship between the graphs of f and f'
   • Graphing the Derivative from Data
   • One-Sided Derivatives

4. Differentiability

   • How f'(a) Might Fail to Exist
   • Differentiability Implies Local Linearity
   • Numerical Derivatives on a Calculator
   • Differentiability Implies Continuity
   • Intermediate Value Theorem for Derivatives

5. Derivatives of Trigonometric Functions

   • Derivative of Sine Function
   • Derivative of Cosine Function
   • Simple Harmonic Motion
   • Derivatives of Other Basic Trigonometric Functions