### 2 videos in "Exponentials / Logarithms"

## The Exponential Function

The Exponential Function

4684 views, 2 ratings - 00:21:11

Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.

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The inverse of the natural logarithm.

- Table of Derivatives - Table of derivatives of several different functions.
- Derivatives and Integrals of exponential function - A list of derivatives and integrals of the exponential function.
- Derivatives and Integrals of exponential and natural logarithm functions - A list of derivatives and integrals of the exponential and natural logarithm function.

- 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.