e^x and ln x
This lesson covers the exponential function e to the x and the natural logarithm function ln x. The number e is defined as the limit of the expression 1 + 1/p^p as p approaches infinity and is approximately equal to 2.71828. The exponential function with base e behaves similarly to other exponential functions, but has important properties such as e to the 0 equals 1 and its derivative is equal to e to the x. The natural logarithm is the inverse of the exponential function, and has a derivative of 1/x. Properties of exponential functions and logarithms are also covered.
Early Transcendental extra video lecture including exponentials and the natural logarithm.
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.
- Derivatives and Integrals of exponential and natural logarithm functions - A list of derivatives and integrals of the exponential and natural logarithm function.
- What is e?
- What is the limit definition of the number e?
- What are the properties of e^x?
- What is the derivative of e^x?
- What is ln x?
- How are e^x and ln x related?
- What are the properties of ln x?
- What is the change of base formula for logarithms and why does it work?
- What is logarithmic differentiation?
- What is the derivative of x^-x?
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Staff Review
This video explains what the number e is, what the limit definition of e is, and what e^x looks like and acts like. Some really high-level proofs are explained in this video. These might be above the level of an ordinary Calculus student. The number e and the exponential function e^x are used to explain ln x, or log base e of x. Properties of logs are explained using rules of exponents.
