Skip to content
Marlow Works

AP Calculus AB / Unit 2

Unit 2 · 10–15%

Differentiation: Definition and Fundamental Properties

The derivative is a limit of average rates. The rules are shortcuts for that limit.

Start first lessonUnit practice

Topics

  • Average versus instantaneous rate
  • The limit definition of the derivative
  • Differentiability and continuity
  • Power, product, and quotient rules

Lessons

Key terms

Original practice

Marlow Works questions. If this unit does not have its own items yet, you will see other questions from the same course.

1 of 1Differentiation: Definition and Fundamental Properties · medium · short answer

If f(x) = 4x³ − 6x + 2, find f′(x).

Original Marlow Works item — not a College Board question.

Take your time—this is practice, not a test.

Review checklist

  1. 01Write a difference quotient before you cancel, if the question is conceptual.
  2. 02State the derivative’s units in a word problem.
  3. 03Check corners and cusps before claiming f′ exists.

Related resources

External links with reuse status. Marlow Works is independent and does not copy restricted exam or textbook material.

  • Official / link only

    AP Calculus AB course page

    Official eight-unit framework and 2027 exam updates.

    College Board · All rights reserved · accessed 2026-10-01

    Open source

  • Reference only — do not copy

    OpenStax College Algebra 2e

    Algebra reference; current terms include noncommercial and AI-ingestion limits.

    OpenStax · Restricted — see publisher page · accessed 2026-10-01

    Open source