Section 3'2 The Exponential Function

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Section 3.2The Exponential Function
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• Consider an exponential graph
• What can we say about the graph of its derivative?

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• Now lets look at using the definition of the
  derivative
• Now, is a constant
• Therefore, the derivative of an exponential is
  proportional to the function itself

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• Let
• For various values of a we get the following
  table
• Notice there is a value of k between 0 and 1

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• So we want
• And we get
• So it is its own derivative

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• Now back to
• We will use the fact that

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• Examples