Understanding Derivatives of Exponential and Logarithmic Functions

1. Photo by Vickie Kelly, 2007 Greg Kelly, Hanford High School, Richland, Washington Mt. Rushmore, South Dakota 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. We can now use this formula to find the derivative of is its own derivative! If we incorporate the chain rule:

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

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

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

10. The formula for the derivative of a log of any base other than e is: To find the derivative of a common log function, you could just use the change of base rule for logs:

11. p