4.1 Assumed knowledge
  4.1.1 First principles definition
  4.1.2 Meaning as slope of a curve
  4.1.3 Differential of a sum
  4.1.4 Differential of product
  4.1.5 Differential of quotient
  4.1.6 Function of a function (chain rule)
  4.1.7 some simple physical examples
  4.1.8 Differential of inverse function
  4.1.9 Maxima and minima
  4.1.10 Higher Derivatives
 4.2 Other techniques
  4.2.1 Implicit Differentiation
  4.2.2 Logarithmic differentiation
  4.2.3 Differentiation of parametric equations
 4.3 Vector functions
  4.3.1 Polar curves
 4.4 Partial derivatives
  4.4.1 Multiple partial derivatives
 4.5 Differentiation and curve sketching
  4.5.1 Global vs. local maximum
  4.5.2 Curve sketching
 4.6 *Application of differentiation: Calculation of small errors*