References: The Derivative Concept
-
Derivative - Wikipedia - Comprehensive overview of the derivative including the limit definition, geometric interpretation as slope, and physical interpretation as rate of change.
-
Tangent - Wikipedia - Explains the tangent line concept from geometric and analytic perspectives. Directly supports the chapter's progression from secant lines to tangent lines.
-
Difference quotient - Wikipedia - Detailed treatment of the difference quotient and its relationship to average and instantaneous rates of change, the foundational formula for this chapter.
-
Calculus: Early Transcendentals (9th Edition) - James Stewart - Cengage Learning - Sections 2.7-2.8 develop the derivative as a limit of slopes with excellent geometric animations described in margin notes.
-
Calculus (3rd Edition) - Michael Spivak - Publish or Perish - Chapter 9 provides a rigorous development of the derivative concept with historical motivation and careful proofs.
-
Definition of the Derivative - Paul's Online Math Notes - Step-by-step examples computing derivatives from the limit definition, with clear algebraic technique demonstrations.
-
Essence of Calculus, Chapter 2: Derivatives - 3Blue1Brown - Beautifully animated explanation of what the derivative truly represents, building geometric intuition beyond formulas.
-
The Derivative as a Function - Khan Academy - Interactive exercises on interpreting the derivative graphically and computing it from the definition.
-
Secant and Tangent Lines - Desmos - Interactive graphing tool showing secant lines approaching the tangent line as h approaches 0, complementing the chapter's MicroSim.
-
Introduction to Derivatives - Math is Fun - Gentle visual introduction to the derivative concept with slope interpretation and step-by-step limit examples.