C3: Differentiation

C3: Differentiation

1. 1: The Derivative

   • 1.1: Tangent to a Planar Curve
   • 1.2: The Derivative at a point
   • 1.3: The Derivative as a Function
     • Notation
       • Lagrange's Prime
       • Leibnitz's
       • Newtonian
   • 1.4: The Linear Approximation
     • Differentials
   • 1.5: Higher-order Derivatives
   • 1.6: Derivative of Simple Functions
     • Power Functions
     • The Power Law
     • Trigonometric Functions
     • Natural Exponential Functions
     • Table of Derivatives
   • 1.7: Differentiability
     • Piecewise-Defined Functions
     • Differentiability => Continuity
     • Non-Differentiability
     • Higher-order Dereivatives
   • 1.8: Continuously Differentiable Functions
     • Comments

2. 2: Rules of Differentiation

   • 2.1: The Sum/Difference Rule
   • 2.2: The Product Rule
   • 2.3: The Quotient Rule

3. 3: Chain Rule & Implicit Differentiation

   • 3.1: Differentiating Compositions
   • 3.2: Examples
   • 3.3: Implicit Differentiation
     • Derivatives of Logarithms
     • Derivatives of Inverse Functions

4. 4: Parametric Curves

   • 4.1: Curves in R^2
     • Examples
   • 4.2 Parametric Differentiation
   • 4.3: Polar Coordinates
     • Polar Equations

5. 5: The Exponential Function

   • 5.1: The Power Series Defintiion
   • 5.2: The Derivative Defintion