Derivatives

Derivatives

1. Rules for differentiation

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

2. Velocity and other rates of change

   • Sensitivity to charge
   • Instantaneous rates of cgange
   • Motion along with a line
   • Derivatives in economics

3. Derivative of a function

   • Notation
   • One-sided derivtives
   • Definition of derivatives
   • Relationship between the graph of f and f'
   • Graphing the derivative form data

4. Differentiality

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

5. Derivatives of trigonometric functions

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