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Unit 2 of 10

Differentiation: Definition and Basic Derivative Rules

This unit introduces the derivative as an instantaneous rate of change and the slope of a tangent line. Students develop derivative notation, estimate derivatives, connect differentiability to continuity, and learn foundational derivative rules.

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UnitsLessons
  1. 01Limits and Continuity16
  2. 02Differentiation: Definition and Basic Derivative Rules10
  3. 03Differentiation: Composite, Implicit, and Inverse Functions6
  4. 04Contextual Applications of Differentiation7
  5. 05Analytical Applications of Differentiation12
  6. 06Integration and Accumulation of Change14
  7. 07Differential Equations9
3 more units in the course outline
Units of AP® Calculus BC

Lessons

10 lessons in this unit

  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 RulePreview 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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