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AP Calculus AB Unit 2: Derivatives
Build fluency in derivative rules, interpretation, and real-world rate-of-change modeling for AP Calculus AB.
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What this unit covers
21 lessons, each with worked examples, practice problems and flashcards.
Derivatives
- What is a Derivative?
Understanding the fundamental concept of derivatives
- The Power Rule
Master the fundamental rule for differentiating polynomial functions
- Derivative Notation
Understanding the different ways to write derivatives
- Derivative as Slope
Understanding derivatives through tangent lines and slope
- Derivative as Rate of Change
Understanding derivatives through real-world rates of change
- The Power Rule
The most fundamental differentiation rule for polynomials
- Constant Multiple and Sum Rules
Essential rules for differentiating linear combinations of functions
- The Product Rule
Differentiating the product of two functions
- The Quotient Rule
Differentiating fractions and rational functions
- The Chain Rule
Finding derivatives of composite functions
- Derivatives of Trigonometric Functions
Finding derivatives of sine, cosine, tangent, and other trig functions
- Derivatives of Exponential Functions
Finding derivatives involving e^x and other exponential functions
- Derivatives of Logarithmic Functions
Finding derivatives involving ln(x) and other logarithmic functions
- Implicit Differentiation
Finding derivatives when y is not isolated
- Related Rates
Finding how rates of change are related to each other
- Higher-Order Derivatives
Second derivatives, third derivatives, and beyond
- Logarithmic Differentiation (Technique)
Using logarithms to simplify difficult differentiation problems
Differentiation Fundamentals
- Definition of the Derivative
Derivative as a limit, differentiability, graphical interpretation, and tangent lines
- Basic Differentiation Rules
Power rule, product rule, quotient rule, trig derivatives, and higher-order derivatives
- Chain Rule
Chain rule, implicit differentiation, and related rates
- Inverse Functions & Derivatives
Derivatives of inverse functions, inverse trig derivatives, and logarithmic differentiation
Common questions
- What does AP Calculus AB Unit 2: Derivatives cover?
- 21 lessons across 2 areas: Derivatives, Differentiation Fundamentals.
- Is AP Calculus AB Unit 2: Derivatives free to study?
- Yes. Every lesson, quiz and set of flashcards on this page is free to use.
- Where should I start?
- Take the diagnostic first so you know which lessons in this unit you can skip, then work the rest in order and finish each with its exit quiz.