Derivatives

Derivatives

1. Differentiability

   • Differentiability implies continuity
   • Intermediate value theorem for derivatives
   • Numerical derivatives on the calculator
   • Differentiability implies local linearity
   • How f(a) might fail to exist

2. Rules for differentiation

   • Positive integer powers, multiples, sun and differences
   • Products and quotients
   • Negative integer powers of x
     • Second and higher order derivatives

3. Derivatives of trigonometric functions

   • The derivative of Sine function
   • Derivative of Sine function
   • Simple harmonic motion
   • Derivative of other basic trigonometric functions

4. Derivative of function

   • One-sided derivatives
   • Definition of derivative
   • Notation
   • Graphing the derivative from data
   • Relationship between the graphs of f and f’

5. Velocity and other rates of change

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