Calculus 1 — 11.1: The Product Rule скачать в хорошем качестве

Calculus 1 — 11.1: The Product Rule

Why can't you just multiply the derivatives of two functions to get the derivative of their product? This video starts with a concrete counterexample — x² times x³ — to show exactly where the naive approach breaks down, then introduces the product rule formula and builds intuition for when and how to apply it. Key concepts covered: • Counterexample disproving the "multiply the derivatives" misconception • The product rule formula: d/dx[f·g] = f'g + fg' • Memory device: "product goes with plus" (and how it contrasts with the quotient rule) • Decision framework: when to use the product rule vs. pulling out a constant • The d/dx bracket notation and how it prevents common errors • Verification technique: combining factors first, then differentiating to confirm ORIGINAL SOURCE This video distills content from a lecture on derivatives. Source video:    • Calculus 1 Lecture 2.3:   The Product and ...   All credit for the original instruction belongs to the original creator.