Chapter 4 More Derivatives Section 4 4 Derivatives

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Chapter 4 More Derivatives Section 4. 4 Derivatives of Exponential and Logarithmic Functions Copyright

Chapter 4 More Derivatives Section 4. 4 Derivatives of Exponential and Logarithmic Functions Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1

Quick Review Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 2

Quick Review Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 2

Quick Review Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 3

Quick Review Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 3

Quick Review Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 4

Quick Review Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 4

Quick Review Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 5

Quick Review Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 5

What you’ll learn about n n n Derivative of ex Derivative of ax Derivative

What you’ll learn about n n n Derivative of ex Derivative of ax Derivative of ln x Derivative of loga x Extending the Power Rule to arbitrary real powers Logarithmic differentiation … and why The relationship between exponential and logarithmic functions provides a powerful differentiation tool called logarithmic differentiation. Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 6

Derivative of ex Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 7

Derivative of ex Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 7

Example Derivative of ex Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 8

Example Derivative of ex Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 8

Derivative of ax Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 9

Derivative of ax Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 9

Derivative of ln x Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 10

Derivative of ln x Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 10

Example Derivative of ln x Copyright © 2016, 2012, and 2010 Pearson Education, Inc.

Example Derivative of ln x Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 11

Derivative of logax Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 12

Derivative of logax Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 12

Rule 10 Power Rule For Arbitrary Real Powers Copyright © 2016, 2012, and 2010

Rule 10 Power Rule For Arbitrary Real Powers Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 13

Example Power Rule For Arbitrary Real Powers Copyright © 2016, 2012, and 2010 Pearson

Example Power Rule For Arbitrary Real Powers Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 14

Logarithmic Differentiation Sometimes the properties of logarithms can be used to simplify the differentiation

Logarithmic Differentiation Sometimes the properties of logarithms can be used to simplify the differentiation process, even if logarithms themselves must be introduced as a step in the process. The process of introducing logarithms before differentiating is called logarithmic differentiation. Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 15

Example Logarithmic Differentiation Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 16

Example Logarithmic Differentiation Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 16

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 17

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 18

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 19

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 20

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 21

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010

Quick Quiz Sections 4. 3 – 4. 4 Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 22

Chapter Test Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 23

Chapter Test Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 23

Chapter Test Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 24

Chapter Test Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 24

Chapter Test Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 25

Chapter Test Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 25

Chapter Test Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 26

Chapter Test Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 26

Chapter Test Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 27

Chapter Test Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 27

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