2. 3.9: Derivatives of Exponential and Logarithmic Functions Mt. Rushmore, South Dakota Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007

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

4. 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.

6. is its own derivative! If we incorporate the chain rule: We can now use this formula to find the derivative of

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

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

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

11. 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:

12. 