Calculating the Derivative

Slides:



Advertisements
Similar presentations
The Quotient Rule Brought To You By Tutorial Services The Math Center.
Advertisements

The Product Rule Brought To You By Tutorial Services The Math Center.
Section 5.4 – Properties of Logarithms. Simplify:
DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.
Chapter 5 Section 1. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. The Product Rule and Power Rules for Exponents Use exponents. Use.
Essential Question: What are some of the similarities and differences between natural and common logarithms.
Homework Read pages 304 – 309 Page 310: 1, 6, 8, 9, 15, 28-31, 65, 66, 67, 69, 70, 71, 75, 89, 90, 92, 95, 102, 103, 127.
Copyright © 2008 Pearson Education, Inc. Chapter 4 Calculating the Derivative Copyright © 2008 Pearson Education, Inc.
Laws (Properties) of Logarithms
4.1 The Product Rule and Power Rules for Exponents.
In this section we will introduce a new concept which is the logarithm
Section 2.4 – The Chain Rule. Example 1 If and, find. COMPOSITION OF FUNCTIONS.
1 The student will learn about: the derivative of ln x and the ln f (x), applications. §3.5 Derivatives of Logarithmic and Exponential Functions. the derivative.
Properties of Logarithms
© 2010 Pearson Education Inc.Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 12e– Slide 1 of 55 Chapter 4 The Exponential and Natural Logarithm.
Section 5.3 Properties of Logarithms Advanced Algebra.
Exponential and Logarithmic Equations
3.6 Derivatives of Logarithmic Functions 1Section 3.6 Derivatives of Log Functions.
How can one use the derivative to find the location of any horizontal tangent lines? How can one use the derivative to write an equation of a tangent line.
Chapter 5 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Example 3 Dividing Mixed Numbers ÷ – 3 19 = 17 6 – Multiply by the reciprocal of 17 6 – 6 – = 3 () 6 – 19 Use rule for multiplying fractions.
Chapter 4 Techniques of Differentiation Sections 4.1, 4.2, and 4.3.
Section 3.4 The Chain Rule. One of THE MOST POWERFUL Rules of Differentiation The chain rule allows you to take derivatives of compositions of functions.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 3 Integration.
Warm Up 2. (3 –2 )(3 5 ) (2 6 )(2 8 ) (7 3 ) Simplify. Write in exponential form. x 0 = 1 6. log x x = 1 x 1 = x 7. 0 =
3.3 Day 1 Properties of logarithms –Use the product rule. –Use the quotient rule. –Use the power rule. –Expand logarithmic expressions. Pg. 407 # 2-36.
Product and Quotient Rule Find the derivative of the function using the Product Rule Find the derivative of the function using the Quotient Rule Find the.
Copyright © Cengage Learning. All rights reserved. 3 Differentiation Rules.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Section 4 Chapter Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Properties of Logarithms Use the product rule for logarithms.
7.2* Natural Logarithmic Function In this section, we will learn about: The natural logarithmic function and its derivatives. INVERSE FUNCTIONS.
Derivatives. Product Rule Quotient Rule The Chain Rule.
Lesson 4 : Exponent Laws I Check it out... Can you see a short cut rule?
4 - 1 © 2012 Pearson Education, Inc.. All rights reserved. Chapter 4 Calculating the Derivative.
8.6 Natural Logarithms.
SECTION 5-1 The Derivative of the Natural Logarithm.
Section 3.1 Derivative Formulas for Powers and Polynomials
§ 4.2 The Exponential Function e x.
Chapter 3 Derivatives.
Copyright © Cengage Learning. All rights reserved.
Derivatives of exponentials and Logarithms
College Algebra Chapter 4 Exponential and Logarithmic Functions
Chapter 3 The Derivative.
Derivatives of Exponential and Logarithmic Functions
Quick Review.
§ 4.5 The Derivative of ln x.
Chapter 1 Functions.
Chapter 1 Functions.
§ 4.4 The Natural Logarithm Function.
Chapter 5 Section 1.
Copyright © Cengage Learning. All rights reserved.
Chapter 3 Derivatives.
Copyright © Cengage Learning. All rights reserved.
Applications of the Derivative
Derivatives of Logarithmic Functions
Copyright © Cengage Learning. All rights reserved.
Chapter 3 Integration Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
College Algebra Chapter 4 Exponential and Logarithmic Functions
Sec 3.6: DERIVATIVES OF LOGARITHMIC FUNCTIONS
Copyright © Cengage Learning. All rights reserved.
4.3 – Differentiation of Exponential and Logarithmic Functions
The Chain Rule Section 3.4.
Copyright © Cengage Learning. All rights reserved.
Derivatives of Exponential and Logarithmic Functions
Derivatives of Exponential and Logarithmic Functions
The Chain Rule Section 2.4.
Chapter 3 Derivatives.
Applied Calculus CH3 Part II Formative
Presentation transcript:

Calculating the Derivative Chapter 4 Calculating the Derivative

Techniques for Finding Derivatives Section 4.1 Techniques for Finding Derivatives

Your Turn 1 Solution:

Your Turn 2 Solution: Rewrite this as,

Your Turn 3 Solution: Rewrite h(t) as

Figure 4

Figure 5

Figure 6

Derivatives of Products and Quotients Section 4.2 Derivatives of Products and Quotients

Your Turn 1 Solution : Simplify by multiplying and combining terms.

Your Turn 2 Solution:

Section 4.3 The Chain Rule

Figure 9

Your Turn 4 Solution:

Your Turn 6 Solution: Now use the product rule and the chain rule.

Derivatives of Exponential Functions Section 4.4 Derivatives of Exponential Functions

Your Turn 1

Your Turn 2 Solution: Use the product rule and the chain rule.

Derivatives of Logarithmic Functions Section 4.5 Derivatives of Logarithmic Functions

Figure 12

Your Turn 1

Your Turn 2 Solution (a): Solution (b):