1. 3.9: Derivatives of Exponential and Logarithmic Functions
Mt. Rushmore, South Dakota
3.9: Derivatives of Exponential and Logarithmic Functions
Created by Greg Kelly, Hanford High School, Richland, Washington
Revised by Terry Luskin, Dover-Sherborn HS, Dover, Massachusetts
Photo by Vickie Kelly, 2001

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,
at x = 0

4. is its own derivative!
If we incorporate the chain rule:
We can also find the derivative of any exponential
function ….

5. It is relatively easy to develop the derivative of any
logarithmic function. The general rules are:

6. The derivations of these rules follow, if you’re interested!

7. Now we work to find a general formula for the derivative of using the limit definition.
This is the slope at x=0, which we have defined to
be 1.

8. We can find the derivative of :
( and are inverse functions.)
(chain rule derivative of eu, where
“inner function” is x ∙ln a )

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

11. To find the derivative of a common log function, you could just use the change of base rule for logs:

12. p