Derivatives

Derivatives

1. Differentiability

   • How f´(a) Might Fall to Exist
   • Intermediate Value Theorem for Derivatives
   • Differentiability Implies Continuity
   • Numerical Derivatives on a Calculator
     • Symmetric difference quotient
     • Numerical derivative of f at a
     • Numerical derivative of f
   • Differentiability Implies Local Linearity
     • Locally linear

2. Derivatives of Trigonometric Functions

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

3. Rules of Differentiation

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

4. Velocity and Other Rates of Change

   • Instantaneous Rates of Change
   • Sensitivity of Change
     • Sensitive
   • Derivatives in Economics
     • Marginal cost
     • Marginal revenue
   • Motion Along a Line
     • Acceleration
     • Speed
     • Displacement
     • Average velocity
     • Instantaneous velocity

5. Derivative of a Function

   • One-Sided Derivatives
     • Left-Hand Derivative at b
     • Right-Hand Derivative at a
     • Differentiable on a closed interval [a,b]
   • Definition of Derivatives
     • f at the point x = a
     • Derivative of f at a
     • Differentiable function
   • Notation
   • Graphing the Derivative from Data
   • Relationship between the graphs of f and f´