Differentiation – definition and fundamental properties

This unit concerns the definition of the derivative and differentiation rules.

Local Linearity 1 – The graphical manifestation of differentiability

Local Linearity II – Connecting local linearity with slope and then the derivative. Graphing calculator hints.

Graphing Calculator use and explorations introducing the derivative

Graphing Calculator Use – (1) Graphing and Store-and-recall

Tangent Line – (2) Exploring the tangent line and the derivative

Seeing Difference Quotients – (3) Using technology to explore difference quotients.

Discovering the Derivative – Ways to introduce the idea of a derivative using a graphing calculator.

Definition of the derivative

The Derivative I – The definition of derivative

The Derivative II – A graphing calculator exploration of difference quotients, introducing the derivative.

Difference Quotients I – The forward and backward difference quotients explained.

Difference Quotients II – The symmetric difference quotient and a calculator or Desmos exercise to watch the three difference quotients converge.

Differentiability Implies Continuity – An important result.  

Differentiation Rules

The Derivative Rules I – Teaching the rules for finding derivatives

The Derivative Rules II – Ways to teach the Product Rule

The Derivative Rules III – Ways to teach the Quotient Rule and a note on using or not using mnemonics.

Why Radians? – Why calculus is done in radians – it’s easier.

The Derivatives of Exponential Functions – Finding the value of e.