Chapter 4 More Derivatives Section 4 4 Derivatives
- Slides: 10
Chapter 4 More Derivatives Section 4. 4 Derivatives of Exponential and Logarithmic Functions Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1
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. 2
Derivative of ex Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 3
Derivative of ax Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 4
Derivative of ln x Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 5
Derivative of logax Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 6
Rule 10 Power Rule For Arbitrary Real Powers Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 7
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. 8
Example Logarithmic Differentiation Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 9
Example 8 n Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 10