Derivates

Derivates

1. Rules of differentiation

   • Products and quotientes
   • Negative integers
   • Positive integer powers multiples sums and differencess
   • Second And higher order derivatives
     • nth derivatives

2. Diferentiability

   • differentianility implies local linearity
     • locally linear
   • Numerical derivatives on a calculator
     • numerical derivative of f
     • numerical derivative of f at a
     • symetric difference quotient
   • how F´(a) Might fall of exist
   • differentiability implies continuity
   • intermediate value theorem of derivatives

3. Derivative of a function

   • Notation
   • Relationship between the graphs of f and f°
   • One-Sided Derivates
     • Left hand derivative at b
     • Right hand derivative at a
     • Differentiable on a closed inteval [a,b]
   • Definition of a Derivative
     • f at the point x = a
     • Differentiable Function
     • Derivative of f at a
   • graphing the derivative form data

4. Derivatives of trigonometric functions

   • Derivatives of the sine function
   • Derivative of the cosine functions
   • Jerk
   • Simple harmonic motion
   • Derivatives of the other basic trigonometric functions

5. Velocity and the other rates of change

   • Motions along the line
     • instantaneous velocity
     • acceleration
     • average velocity
     • Displacement
     • speed
   • Derivatives in economics
     • marginal revenue
     • marginal cost
   • Indstataneous rates of change
   • sensitivity to change
     • sensitive