Chapter 4 More Derivatives Section 4 4 Derivatives

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. 3

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

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 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

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

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

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 Education, Inc. 14

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

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 Pearson Education, Inc. 18

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 Pearson Education, Inc. 20

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 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. 24

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. 27