The Product Rule: Why Multiplying Derivatives Doesn't Work

Описание: 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.

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