3.9: Derivatives of Exponential and Logarithmic Functions

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# 3.9: Derivatives of Exponential and Logarithmic Functions - PowerPoint PPT Presentation

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

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Photo by Vickie Kelly, 2007

Greg Kelly, Hanford High School, Richland, Washington

Mt. Rushmore, South Dakota

3.9: Derivatives of Exponential and Logarithmic Functions

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.

We can now use this formula to find the derivative of

is its own derivative!

If we incorporate the chain rule:

( is a constant.)

Incorporating the chain rule:

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