3.5 The Chain Rule

OpenStax Calculus Volume 1 — Section 3.5

Learning Objectives

  • State the chain rule: \(\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)\)

  • Identify the outer and inner functions in a composition

  • Apply the chain rule to nested compositions (multiple layers)

  • Combine chain rule with product, quotient, and trig derivative rules

Key Concepts

To be filled during study.

Practice Problems

To be completed with textbook exercises.

Section Summary

To be written after completing the section.

Study Notes

Personal observations and connections to engineering work.