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3.7: Derivatives of Exponential and Logarithmic Functions

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1 3.7: Derivatives of Exponential and Logarithmic Functions
Mt. Rushmore, South Dakota 3.7: Derivatives of Exponential and Logarithmic Functions Greg Kelly, Hanford High School, Richland, Washington 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

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.

4

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

9

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


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