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 Derivative of log a x

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

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

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