1. Derivatives of Exponential and Logarithmic Functions
Section 3.9

2. Look at the graph of
If we assume this to be true, then:
The slope at x=0 appears to be 1.
definition of derivative

3. Now we attempt to find a general formula for the derivative of using the definition.
This is the slope at x=0, which we have assumed to be 1.

5. is its own derivative!
If we incorporate the chain rule:

6. Example:

7. Deriving Another Formula:
( and are inverse functions.)
(chain rule)

8. ( is a constant.)
Incorporating the chain rule:

9. Example:

10. So far today we have:
Now it is relatively easy to find the derivative of

11. Deriving Another Formula:

12. Example:

13. Deriving Another Formula:
To find the derivative of a common log function, you could just use the change of base rule for logs:
The formula for the derivative of a log of any base other than e is:

14. Example:

15. p

16. Homework