1. 3.9: 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:
We can now use this formula to find the derivative of

6. ( and are inverse functions.)
(chain rule)

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

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

10. 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:

11. p

12. Homework:
3.9a 3.9 p178 3,12,21,30,39
3.8 p170 24,41
2.4 p92 11,29
3.9b 3.9 p178 6,15,24,27,33,42,49,55,64

13. Review:
p multiples of 3
(practice test – extra credit)
TEST: Ch. 3 & 2