Derivatives

Derivatives

1. Derivate of a Function

   • Definition of Derivates
   • Graphing the Derivate from Data
   • Relationship between the graphs of f and f
   • One-sided Derivates
   • Notation

2. Velocity and other rates of change

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

3. Differentiability

   • Differentiability implies continuity
   • How f´(a) Might Fail to Exist
   • Intermediate Value Theorem for Derivates
   • Numerical Derivates on a Calculator
   • Differentiability implies Local Linearity

4. Rules of Differentiation

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

5. Derivatives of Trigonometric Functions

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