Calc03 9

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Calc03 9

  1. 1. 3.9: Derivatives of Exponential and Logarithmic Functions Mt. Rushmore, South Dakota
  2. 2. Look at the graph of The slope at x=0 appears to be 1. If we assume this to be true, then: definition of derivative
  3. 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
  5. 6. (chain rule) ( and are inverse functions.)
  6. 7. Incorporating the chain rule: ( is a constant.)
  7. 8. So far today we have: Now it is relatively easy to find the derivative of .
  8. 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:
  9. 11.

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