chapter 2

Chapter 2

Differentiation

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Figure 2.1: Tangent Line to a Graph


Figure 2.2: Tangent Lineto a Graph at a Point


Figure 2.3: Tangent Line to a Circle


Figure 2.6: The SecantLine Through the Two Points


Figure 2.7: Secant lineapproaches the tangent line


Definition of the Slope of a Graph


Definition of the Derivative


Figure 2.11: Functions ThatAre Not Differentiable at x = 0


Differentiability Implies Continuity


Figure 2.12: The Constant Rule


Figure 2.13: The (Simple)Power Rule


The Constant Multiple Rule


The Sum and Difference Rules


Figure 2.18: Definition ofAverage Rate of Change


Definition ofInstantaneous Rate of Change


Marginal Profit/Marginal Revenue/Marginal Cost


Figure 2.22: Discrete andContinuous Variables


The Product Rule


The Quotient Rule


Figure 2.28: The Chain Rule


The General Power Rule


Summary of Differentiation Rule


Notation forHigher-Order Derivatives


Position Function/Velocity Function/Acceleration Function


Implicit Differentiation


Guidelines for Solvinga Related-Rate Problem


Table: Verbal Statement/Mathematical Model


Simplifying Algebraic Expressions

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