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References: The Derivative Concept

  1. Derivative - Wikipedia - Comprehensive overview of the derivative including the limit definition, geometric interpretation as slope, and physical interpretation as rate of change.

  2. Tangent - Wikipedia - Explains the tangent line concept from geometric and analytic perspectives. Directly supports the chapter's progression from secant lines to tangent lines.

  3. 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.

  4. 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.

  5. Calculus (3rd Edition) - Michael Spivak - Publish or Perish - Chapter 9 provides a rigorous development of the derivative concept with historical motivation and careful proofs.

  6. Definition of the Derivative - Paul's Online Math Notes - Step-by-step examples computing derivatives from the limit definition, with clear algebraic technique demonstrations.

  7. Essence of Calculus, Chapter 2: Derivatives - 3Blue1Brown - Beautifully animated explanation of what the derivative truly represents, building geometric intuition beyond formulas.

  8. The Derivative as a Function - Khan Academy - Interactive exercises on interpreting the derivative graphically and computing it from the definition.

  9. Secant and Tangent Lines - Desmos - Interactive graphing tool showing secant lines approaching the tangent line as h approaches 0, complementing the chapter's MicroSim.

  10. Introduction to Derivatives - Math is Fun - Gentle visual introduction to the derivative concept with slope interpretation and step-by-step limit examples.