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Study Guide — Differentiation — Definition and Fundamental Properties

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Calculus AB · AP

AP-aligned study guide for Differentiation — Definition and Fundamental Properties.

What this standard means

  • Defining Average and Instantaneous Rates of Change at a Point CHA-2 Derivatives allow us to determine rates of change at an instant by apply
  • Defining the Derivative of a Function and Using Derivative Notation CHA-2 Derivatives allow us to determine rates of change at an instant by
  • Estimating Derivatives of a Function at a Point § Classroom Resource > Approximation
  • Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
  • Applying the Power Rule FUN-3 Recognizingopportunitiestoapplyderivativerulescansimplifydifferentiation.
  • Derivative Rules: Constant, Sum, Difference, and Constant Multiple FUN-3

_See printable PDF for diagram._

How to use the 20 practice sets

| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |

Pacing: 10–15 minutes per session.

How to practice

1. Sketch graphs to check signs and behavior 2. Label u-substitution clearly 3. Interpret derivatives and integrals in context

_See printable PDF for diagram._

Common mistakes

  • Algebra errors after differentiation
  • Forgetting +C
  • Misapplying L'Hôpital

Review and practice tests

1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for Differentiation — Definition and Fundamental Properties.

  • [ ] Computes limits and derivatives accurately
  • [ ] Sets up and evaluates definite integrals
  • [ ] Explains results in applied settings

Materials for this standard

  • Practice Problems — 20 printable sets
  • Review — 10 difficulty levels
  • Practice Test — 10 difficulty levels
  • Answer key — for parents and tutors

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