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2.2 Defining the Derivative of a Function

AP Calculus AB

Defining the Derivative

The derivative as a limit

Alternative form

The derivative as a function

Worked example: finding $f'(x)$ from the definition

Worked example: $f(x) = \sqrt{x}$

Worked example: $f(x) = \dfrac{1}{x}$

procedure for limit definition problems

Recognizing limits as derivatives

The tangent line equation

Example: tangent line

AP exam tips

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Vocabulary

Unit 2 topics

Unit 2 overview12.1 Defining Average and Instantaneous Rates of Change22.2 Defining the Derivative of a Function32.3 Using Derivative Notation42.4 Estimating Derivatives at a Point52.5 Connecting Differentiability and Continuity62.6 Applying the Power Rule72.7 Derivative Rules: Constant, Sum, Difference, and Constant Multiple82.8 Connecting Derivative Rules with the Power Rule92.9 Derivatives of sin(x), cos(x), eˣ, and ln(x)102.10 The Product Rule112.11 The Quotient Rule122.12 Derivatives of tan(x), cot(x), sec(x), and csc(x)
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