Derivatives

Derivatives

1. Velocity and other rates of change

   • motion along a line
   • Instantaneous rates of change
   • Derivatives in economics
   • sensitivity to change

2. Rules for differentiation

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

3. Differentiability

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

4. Derivative of a function

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

5. Derivatives of trigonometric functions

   • Derivatives of cosine functions
   • derivatives of other basic trigonometric functions
   • Derivative of sine function
   • Simple armonic motion