1. Derivatives of Exponential and Logarithmic Functions
AP Calculus AB
Derivatives of Exponential and Logarithmic Functions

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 1

7. Example 2

8. We can now use this formula to find the derivative of
( and are inverse functions.)
(chain rule)

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

10. Example 3

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

13. 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. p

15. Example 4
= 1

16. Example 5
= 1

17. Example 6

18. Example 7
First, take the ln of both sides.

19. Example 7 (cont.)