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.
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.