# Calculus Chapter 5 Day 1 1. The Natural Logarithmic Function and Differentiation The Natural Logarithmic Function- The number e- The Derivative of the.

## Presentation on theme: "Calculus Chapter 5 Day 1 1. The Natural Logarithmic Function and Differentiation The Natural Logarithmic Function- The number e- The Derivative of the."— Presentation transcript:

Calculus Chapter 5 Day 1 1

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

The Natural Logarithmic Function 3

Definition of the Natural Logarithmic Function 4

Properties of the Natural Logarithmic Function 5

Logarithmic Properties 6

7

8

Derivative of the Natural Logarithmic Function 9

10

Derivative Involving Absolute Value 11

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

Log Rule for Integration 13

Log Rule for Integration 14

Integrals of Trigonometric Functions 16

Integrals of the Six Basic Trigonometric Functions 17

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

Inverse Functions 19

Definition of an Inverse Function 20

Reflective Property of Inverse Functions 21

Existence of an Inverse Function 22

The Existence of an Inverse Function 23

Guidelines for Finding the Inverse of a Function 24

Derivative of an Inverse Function 25

Continuity and Differentiability of Inverse Functions 26

The Derivative of an Inverse Function 27

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

The Natural Exponential Function 29

Definition of the Natural Exponential Function 30

Inverse Relationships 31

Operations with Exponential Functions 32

Properties of the Natural Exponential Function 33

Derivatives of Exponential Functions 34

The Derivative of the Natural Exponential Function 35

Integrals of Exponential Functions 36

Integration Rules for Exponential Functions 37

39

40

41

42

Properties of Inverse Functions 43

Differentiation and Integration 44

45

Integration 46

The Power Rule for Real Exponents 47

Applications of Exponential Functions 48

49

Summary of Compound Interest Formulas 50