# Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivatives of Exponential and Logarithmic Functions Section 3.9.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Derivatives of Exponential and Logarithmic Functions Section 3.9

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 2 Quick Review

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 3 Quick Review

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 4 What you’ll learn about Derivative of e x Derivative of a x Derivative of ln x Derivative of log a x Power Rule for Arbitrary Real Powers … and why The relationship between exponential and logarithmic functions provides a powerful differentiation tool called logarithmic differentiation.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 5 Derivative of e x

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 6 Example Derivative of e x

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 7 Derivative of a x

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 8 Derivative of ln x

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 9 Example Derivative of ln x

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 10 Derivative of log a x

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 11 Example Power Rule For Arbitrary Real Powers

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 12 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 © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 3- 13 Example Logarithmic Differentiation

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Page 170 (1-41 odd, 47) Slide 3- 14