Derivatives

Derivatives

1. Derivative of a Function

   • Relationships between the graphs of f and f'
   • One-sided Derivatives
   • Notation
   • Definition of Derivative
   • Graphing the derivative from data

2. Rules for differentiation

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

3. Velocity and Other Rates of change

   • Derivatives in Economics
   • Instantaneous rates of Change
   • Sensitivity to change
   • Motion along a line

4. Derivatives of Trigonometric Functions

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

5. Differentiability

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

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