Derivatives

Derivatives

1. Differentiability

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

2. Rules for Differentiation

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

3. Derivatives of Trigonometric Functions

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

4. Derivative of a function

   • Definition of Derivative
     • Derivative of f at a
     • Differentiable fuction
     • f at the point x = a
   • Notation
   • RelationshipsBetween the Graphs of f and f '
   • Graphing the Derivative from Data
   • One-Sided Derivatives
     • Differentiable on a closed interval [a,b]
     • Right-hand derivative at a
     • Left-hand derivative at b

5. Velocity and Other Rates of Change

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