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Calculus Chapter 5 Day 1 1

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The Natural Logarithmic Function and Differentiation The Natural Logarithmic Function- The number e- The Derivative of the Natural Logarithmic Function 2

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The Natural Logarithmic Function 3

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Definition of the Natural Logarithmic Function 4

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Properties of the Natural Logarithmic Function 5

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Logarithmic Properties 6

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Derivative of the Natural Logarithmic Function 9

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Derivative Involving Absolute Value 11

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The Natural Logarithmic Function and Integration Log Rule for Integration- Integrals of Trigonometric Functions 12

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Log Rule for Integration 13

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Log Rule for Integration 14

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Practice ▪ Click Here for Assignment 5-1: Assignment 5-1 15

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Integrals of Trigonometric Functions 16

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Integrals of the Six Basic Trigonometric Functions 17

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Inverse Functions Inverse Functions- Existence of an Inverse Function- Derivative of an Inverse Function 18

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Inverse Functions 19

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Definition of an Inverse Function 20

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Reflective Property of Inverse Functions 21

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Existence of an Inverse Function 22

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The Existence of an Inverse Function 23

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Guidelines for Finding the Inverse of a Function 24

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Derivative of an Inverse Function 25

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Continuity and Differentiability of Inverse Functions 26

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The Derivative of an Inverse Function 27

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Exponential Functions: Differentiation and Integration The Natural Exponential Function- Derivatives of Exponential Functions- Integrals of Exponential Functions 28

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The Natural Exponential Function 29

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Definition of the Natural Exponential Function 30

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Inverse Relationships 31

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Operations with Exponential Functions 32

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Properties of the Natural Exponential Function 33

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Derivatives of Exponential Functions 34

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The Derivative of the Natural Exponential Function 35

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Integrals of Exponential Functions 36

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Integration Rules for Exponential Functions 37

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Practice ▪ Click Here for Assignment 5-2 Assignment 5-2 38

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Properties of Inverse Functions 43

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Differentiation and Integration 44

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Integration 46

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The Power Rule for Real Exponents 47

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Applications of Exponential Functions 48

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Summary of Compound Interest Formulas 50

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Practice ▪ Click Here for Assignment 5-3 Assignment 5-3 51

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