The Exponential Function

The Exponential Function
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Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at
The inverse of the natural logarithm.
  • What is the exponential function?
  • What is the definition of e?
  • What is the inverse of ln x?
  • What is the derivative of e^x?
  • What is the derivative of e^u?
  • What is the integral of e^u?
  • What is the integral of e^kx?
  • What is the derivative and integral of b^x?
  • What is the change of base formula for logarithms?
The number e and the exponential e^x are defined and explained. Also, the inverse of the natural logarithm is discovered and explained with graphs and animations. Properties of the natural logarithm and the exponential function are explained. Several examples of finding the derivative of e^u for various u functions are shown. We also see how to sketch the graph of f(x) = x^2e^-x. A really great, comprehensive video on logarithms.
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Reviewed by MathVids Staff on December 20, 2008.
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