Section 6.2* The Natural Logarithmic Function. THE NATURAL LOGARITHMIC FUNCTION.

Slides:



Advertisements
Similar presentations
The Natural Logarithmic Function
Advertisements

Section 5.4 – Properties of Logarithms. Simplify:
7.1 – The Logarithm Defined as an Integral © 2010 Pearson Education, Inc. All rights reserved.
© 2010 Pearson Education, Inc. All rights reserved.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivatives of Exponential and Logarithmic Functions Section 3.9.
Calculus Chapter 5 Day 1 1. The Natural Logarithmic Function and Differentiation The Natural Logarithmic Function- The number e- The Derivative of the.
Aim: Differentiating Natural Log Function Course: Calculus Do Now: Aim: How do we differentiate the natural logarithmic function? Power Rule.
3.9 Derivatives of Exponential and Logarithmic Functions.
3.9 Derivatives of Exponential and Logarithmic Functions.
1 Logarithms Definition If y = a x then x = log a y For log 10 x use the log button. For log e x use the ln button.
The Natural Logarithmic Function
Derivative of Logarithmic Function.
3.6 Derivatives of Logarithmic Functions 1Section 3.6 Derivatives of Log Functions.
The Natural Logarithmic Function
Special Derivatives. Derivatives of the remaining trig functions can be determined the same way. 
Logarithmic, Exponential, and Other Transcendental Functions 5 Copyright © Cengage Learning. All rights reserved.
Logarithmic, Exponential, and Other Transcendental Functions 5 Copyright © Cengage Learning. All rights reserved.
CHAPTER 5 SECTION 5.5 BASES OTHER THAN e AND APPLICATIONS.
Copyright © Cengage Learning. All rights reserved. Logarithmic, Exponential, and Other Transcendental Functions.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 3 Integration.
Section 5.1 The Natural Log Function: Differentiation
3.9 Derivatives of Exponential and Logarithmic Functions.
Table of Contents Logarithm Properties - Product Rule The Product Rule for logarithms states that... read as “the log of the product is the sum of the.
Section 3.4 The Chain Rule. Consider the function –We can “decompose” this function into two functions we know how to take the derivative of –For example.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 6.3 Antidifferentiation by Parts.
5-1: Natural Logs and Differentiation Objectives: ©2003Roy L. Gover ( Review properties of natural logarithms Differentiate natural logarithm.
Chapter 4 Additional Derivative Topics Section 4 The Chain Rule.
Logarithmic, Exponential, and Other Transcendental Functions
Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 6.4 Fundamental Theorem of Calculus Applications of Derivatives Chapter 6.
5.3 – The Fundamental Theorem of Calculus
5.3 Definite Integrals and Antiderivatives. What you’ll learn about Properties of Definite Integrals Average Value of a Function Mean Value Theorem for.
Logarithmic Functions. Examples Properties Examples.
6.3 Antidifferentiation by Parts Quick Review.
Logarithmic, Exponential, and Other Transcendental Functions
Chapter 5 Logarithmic, Exponential, and Other Transcendental Functions.
Table of Contents Logarithm Properties - Quotient Rule The Quotient Rule for logarithms states that... read as “the log of the quotient is the difference.
Derivatives. Product Rule Quotient Rule The Chain Rule.
SECTION 5-1 The Derivative of the Natural Logarithm.
Section 5.4 Exponential Functions: Differentiation and Integration.
SECTION 5-5A Part I: Exponentials base other than e.
5 Logarithmic, Exponential, and Other Transcendental Functions
Chapter 3 Derivatives.
Derivatives of Logarithmic Functions
Chain Rules for Functions of Several Variables
Derivatives of Exponential and Logarithmic Functions
Quick Review.
Definite Integrals and Antiderivatives
Derivatives and Integrals of Natural Logarithms
Mathboat.com.
General Logarithmic and Exponential Functions
Chapter 3 Derivatives.
Derivatives of Logarithmic Functions
2.4 The Chain Rule Use the Chain Rule to find derivative of a composite function. Use the General Power Rule to find derivative of a function. Simplify.
EXPONENTIAL FUNCTIONS: DIFFERENTIATION AND INTEGRATION
Chapter 3 Integration Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Section 5.3 Definite Integrals and Antiderivatives
5 Logarithmic, Exponential, and Other Transcendental Functions
Definite Integrals and Antiderivatives
4.3 – Differentiation of Exponential and Logarithmic Functions
Differentiate the function:    {image} .
The Derivatives of ax and logax
Derivatives of Exponential and Logarithmic Functions
Definite Integrals & Antiderivatives
Derivatives of Exponential and Logarithmic Functions
Group Thinking – CIC Problem
Chapter 3 Derivatives.
Antidifferentiation by Substitution
Antidifferentiation by Parts
Fundamental Theorem of Calculus
Section 5.6 – Properties of Logarithms
Presentation transcript:

Section 6.2* The Natural Logarithmic Function

THE NATURAL LOGARITHMIC FUNCTION

THE DERIVATIVE OF THE NATURAL LOGARITHMIC FUNCTION

LAWS OF LOGARITHMS

PROPERTIES OF THE NATURAL LOGARITHMIC FUNCTION

THEOREM

THE NUMBER e Definition: e is the number such that ln e = 1 e ≈

THE DERIVATIVE OF THE NATURAL LOGARITHM AND THE CHAIN RULE

ANTIDERIVATIVES INVOLVING THE NATURAL LOGARITHM Theorem:

ANTIDERIVATIVES OF SOME TRIGONOMETRIC FUNCTIONS

LOGARITHMIC DIFFERENTIATION