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3.9: Derivatives of Exponential and Logarithmic Functions

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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3.9: Derivatives of Exponential and Logarithmic Functions

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  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.

  4. We can now use this formula to find the derivative of is its own derivative! If we incorporate the chain rule:

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

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

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

  8. 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:

  9. p

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