2. 3.9 Derivatives of Exponential and Logarithmic Functions

3. Quick Review

5. Quick Review Solutions

7. 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 Essential Question How do we use the relationship between exponential and logarithmic functions to provide a powerful differentiation tool called logarithmic differentiation?

8. Derivative of e x Example Derivative of e x 1.

9. Derivative of a x Example Derivative of a x

10. Derivative of ln x Example Derivative of ln x 3.

11. Derivative of log a x Example Derivative of log a x

12. Rule 10 Power Rule For Arbitrary Real Powers Example Power Rule for Arbitrary 5.

13. 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.

14. Example Logarithmic Differentiation 6.

15. Pg. 178, 3.9 #1-47 odd