Calculus 1 — 14.1: The Chain Rule
How do you differentiate (3x² − 4)¹⁰⁰ without expanding 201 terms? This video introduces the chain rule for composite functions — identifying an outer and inner function, differentiating each, and multiplying the results. You'll see how the general power rule emerges as a direct application and why the ordinary power rule was secretly the chain rule all along.
Key concepts covered:
• Recognizing composite functions using the cover-up technique to identify outer and inner functions
• The chain rule in Leibniz notation: dy/dx = dy/du · du/dx and the du cancellation mnemonic
• Step-by-step differentiation of (3x² − 4)¹⁰⁰ using the chain rule
• The general power rule: d/dx [f(x)]ⁿ = n·[f(x)]ⁿ⁻¹·f′(x) and why forgetting f′(x) gives a fundamentally wrong answer
• How the ordinary power rule is a special case of the chain rule where f(x) = x and f′(x) = 1
• Practice problem: differentiating (5x³ + 1)⁴ with a three-step checklist
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SOURCE MATERIALS
The source materials for this video are from • Calculus 1 Lecture 2.6: Discussion of the...