References: The Chain Rule

1. Chain rule - Wikipedia - Formal statement, multiple proofs, and applications of the chain rule including higher dimensions. Core reference for the composition-based differentiation technique in this chapter.

2. Function composition - Wikipedia - Explains how functions combine and the notation used. Essential prerequisite background for understanding why the chain rule is needed.

3. Faà di Bruno's formula - Wikipedia - Generalization of the chain rule to higher-order derivatives of compositions. Provides deeper mathematical context for advanced students.

4. Calculus: Early Transcendentals (9th Edition) - James Stewart - Cengage Learning - Section 3.4 presents the chain rule with the "outside-inside" strategy, Leibniz notation version, and extensive composite function examples.

5. Thomas' Calculus (15th Edition) - Joel Hass, Christopher Heil, Maurice Weir - Pearson - Section 3.6 develops the chain rule with both prime and Leibniz notation, emphasizing pattern recognition for nested compositions.

6. Chain Rule - Paul's Online Math Notes - Comprehensive examples organized by complexity, from simple compositions to deeply nested functions with multiple rule applications.

7. Chain Rule Practice - Khan Academy - Progressive practice problems on identifying inside and outside functions and applying the chain rule, aligned to AP curriculum.

8. Essence of Calculus: Chain Rule - 3Blue1Brown - Visual explanation of why the chain rule works using the idea of composing small changes, building geometric understanding.

9. Chain Rule Examples - Math is Fun - Step-by-step chain rule examples with clear identification of inner and outer functions, ideal for initial practice.

10. Nested Chain Rule Problems - Whitman College Calculus - Open-source section with increasingly complex chain rule exercises requiring multiple rule combinations.