1. Quick Review

2. Quick Review Solutions

3. Quick Review

4. Quick Review Solutions

5. Derivatives of Exponential and Logarithmic Functions
3.9
Derivatives of Exponential and Logarithmic Functions

6. What you’ll learn about
Derivative of ex
Derivative of ax
Derivative of ln x
Derivative of logax
Power Rule for Arbitrary Real Powers
… and why
The relationship between exponential and logarithmic functions provides a powerful differentiation tool called logarithmic differentiation.

7. Derivative of ex

8. Example Derivative of ex

9. Derivative of ax

10. Derivative of ln x

11. Example Derivative of ln x

12. Derivative of logax

13. Rule 10 - Power Rule For Arbitrary Real Powers
If u is a positive differentiable function of x and n is a real number, then

14. Example Power Rule For Arbitrary Real Powers

15. 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.

16. Example Logarithmic Differentiation

17. Example Logarithmic Differentiation

18. Quick Quiz Sections 3.7 – 3.9

19. Quick Quiz Sections 3.7 – 3.9

20. Quick Quiz Sections 3.7 – 3.9

21. Quick Quiz Sections 3.7 – 3.9

22. Quick Quiz Sections 3.7 – 3.9

23. Quick Quiz Sections 3.7 – 3.9