Derivatives

Derivatives

1. Derivative of a funtion

   • Derivative of f at a
   • Derivative
     • Derivative at a point
       • f at the point x=a
   • If f (x) exists, (f has a derivative (is differentiable)
     • A funtion that is differenciable at every point of its domain is a "differenciable funtion"
   • Notation
   • Relationship between the graphs of f and f´
     • Graphing the drerivative from data
   • One- side derivatives
     • A funtion y= f (x) is "differentiable on a closed interval [a,b]
       • Left- hand derivative at b
       • Right-hand derivative at a

2. Differentiability

   • Implies local linearity
     • locally linear
   • Numerical Derivatives
     • symmetric difference quotient
     • numerical derivative of f at a
     • numerical derivative of f
   • Implies continuity
   • Intermediate value theorem for derivatives

3. Rules for differentiation

   • Positive, Integer power, Multiples, Sums, and Differences
     • 1.Derivative of a constant funtion
     • 2. Power rule for positive integer powers of x
       • 3. The constant multiple rule
         • 4.Sum and difference rule
   • Products and Quotients
     • 5. The product rule
       • 6. The quotient rule
   • Negative integer power of x
     • 7. Power rule for negative integer powers of x
   • Second and higher order derivatives
     • nth derivative

4. Derivatives of trigonometric funtions

   • Derivative of a sine funtion
     • Derivative of a cosine funtion
   • Jerk (derivative of acceleration)
     • Simple harmonic motion
       • Derivatives of the others basic trigonometric funtions

5. Velocity and other rates of change

   • Instantaneous rate of change
     • Motion along a line
       • displacement
       • Average velocity
       • Instantaneous velocity
       • Speed
       • Acceleration
   • Sensivity to change
     • Sensivity
   • Derivatives in economics
     • marginal cost
     • marginal revenue