1. 3.9: Derivatives of Exponential and Logarithmic Functions
Mt. Rushmore, South Dakota
3.9: Derivatives of Exponential and Logarithmic Functions
Greg Kelly, Hanford High School, Richland, Washington
Photo by Vickie Kelly, 2007

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