Derivatives of Exponential and Logarithmic Functions

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Presentation transcript:

Derivatives of Exponential and Logarithmic Functions Section 3.9

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

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.

is its own derivative! If we incorporate the chain rule:

Example:

Deriving Another Formula: ( and are inverse functions.) (chain rule)

( is a constant.) Incorporating the chain rule:

Example:

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

Deriving Another Formula:

Example:

Deriving Another Formula: 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:

Example:

p

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