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Chapter 2

Differentiation

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Tangent Line to a Graph

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Tangent Line to a Circle

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Tangent Lineto a Graph at a Point

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The SecantLine Through the Two Points

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Secant lineapproaches the tangent line

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Definition of the Slope of a Graph

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Definition of the Derivative

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Functions ThatAre Not Differentiable at x = 0

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The Constant Rule

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The (Simple)Power Rule

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The Constant Multiple Rule

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The Sum and Difference Rules

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Definition ofAverage Rate of Change

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Definition ofInstantaneous Rate of Change

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The Product Rule

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The Quotient Rule

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The Chain Rule

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The General Power Rule

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Summary of Differentiation Rule

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Marginal Profit/Marginal Revenue/Marginal Cost

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Notation forHigher-Order Derivatives

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Position Function/Velocity Function/Acceleration Function

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Implicit Differentiation

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Table: Verbal Statement/Mathematical Model

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Guidelines for Solvinga Related-Rate Problem

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