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2.8 The Product Rule

Part of Differentiation: Definition and Basic Derivative Rules in AP® Calculus AB. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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The product rule is used when a function is written as one function multiplied by another. If
y=f(x)g(x)y=f(x)g(x)
then its derivative is
y′=f′(x)g(x)+f(x)g′(x)y'=f'(x)g(x)+f(x)g'(x)

You cannot simply multiply the derivatives of the two factors, because the rate of change of a product depends on how both factors are changing together. The product rule accounts for both contributions: one term keeps the second factor unchanged while differentiating the first, and the other term keeps the first factor unchanged while differentiating the second.

In this unit

10 lessons

  1. 2.1Defining Average and Instantaneous Rates of Change at a PointPreview lesson
  2. 2.2Defining the Derivative of a Function and Using Derivative NotationPreview lesson
  3. 2.3Estimating Derivatives of a Function at a PointPreview lesson
  4. 2.4Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not ExistPreview lesson
  5. 2.5Applying the Power RulePreview lesson
  6. 2.6Derivative Rules: Constant, Sum, Difference, and Constant MultiplePreview lesson
  7. 2.7Derivatives of cos x, sin x, eˣ, and ln xPreview lesson
  8. 2.8The Product RuleThis lesson
  9. 2.9The Quotient RulePreview lesson
  10. 2.10Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant FunctionsPreview lesson

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