derivates

derivates

1. derivates of trigonometric functions

   • derivative of sine function
   • derivative of cosine function
   • simple harmonic motion
   • derivatives of other basic trigonometric functions

2. differentiablity

   • differentiability implies local linearity
   • numerical derivatives on a calculator
   • differentiability implies continuity
   • intermediate value theorem for derivatives
   • how f(a) might fail to exist

3. rules for differentiation

   • products of quotients
   • negative integer powers of x
   • second and higher-order derivatives
   • positive integer powers, multiples, sums and differences

4. velocity and other rates of change

   • motion along a line
   • sensitivity to change
   • instantaneous rates of change
   • derivatives in economics

5. derivative of a function

   • notation
   • relationships between the graphs of f and f'
   • graphing the derivative from data
   • one-sided derivatives
   • definition of derivatives