AP®︎ Calculus AB Unit 2: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 2 of AP Calculus AB – Differentiation: Definition and Fundamental Properties.
Unit 2: Differentiation: Definition and Fundamental Properties
Define the derivative using limits and learn fundamental differentiation rules.
Begin with Topic 2.1: Defining Average and Inst...To review Unit 2, go through each of the 10 topics below.
Everything you actually need to know for your Unit 2 test, pulled directly from the AP® Calculus AB curriculum.
Defining Average and Instantaneous Rates of Change at a Point
Defining Average and Instantaneous Rates of Change at a Point
- Average Rate of Change
- Instantaneous Rate of Change and the Derivative at a Point
- Computing the Derivative from the Definition
Defining the Derivative of a Function and Using Derivative Notation
Defining the Derivative of a Function and Using Derivative Notation
- The Derivative as a Limit
- What the Difference Quotient Is Really Doing
- Computing a Derivative from the Definition
Estimating Derivatives of a Function at a Point
Estimating Derivatives of a Function at a Point
- What the Derivative at a Point Represents
- Estimating from a Table of Values
- Estimating from a Graph
Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
- Differentiability and Continuity at a Point
- What Must Be True for a Derivative to Exist
- When a Function Is Not Differentiable
Applying the Power Rule
Applying the Power Rule
- The Power Rule
- Applying the Power Rule Correctly
- Polynomials and Constants
Derivative Rules: Constant, Sum, Difference, and Constant Multiple
Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- The Four Linearity Rules
- The Big Picture: Linearity
- Combining These with the Power Rule
Derivatives of cos x, sin x, e^x, and ln x
Derivatives of cos x, sin x, e^x, and ln x
- The Core Derivative Facts You Must Know Cold
- Using These Rules Inside Larger Expressions
- Common Errors That Cost Points
The Product Rule
The Product Rule
- The Product Rule
- Why This Rule Exists
- Recognizing When to Use It
The Quotient Rule
The Quotient Rule
- The Quotient Rule
- What the Rule Is Actually Doing
- When to Use It vs When to Rewrite
Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
- The Derivatives of tan x, cot x, sec x, and csc x
- Rewriting Trig Functions Using Identities
- Applying the Derivative Rules
Notes
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