## Exponential Function - Differential Equations in Action

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Euler's number and the exponential function based on that number are of vital importance in the theory of differential equations.
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Whenever we are dealing with exponential growth or exponential decay, and whenever we deal with oscillations,
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Euler's number plays a big role. This is a brief and informed introduction to that topic, for which we need a minimum
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amount of prerequisites. In particular, you should know that five to the first power equals five.
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Five to the zeroth power equals one. Five to the minus second power equals one over 25.
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Five to the power of one half equals the square root of five.
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Five to the third power times five to the fourth power equals five to the power of three plus four--seven.
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And five to the third power to the fourth power equals five to the power of 12--three times four.
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This is what you need to know about powers of numbers.
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In addition, you should have an idea about derivatives in this D, DX notation--for instance, the derivate of X squared
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with respect to X equals 2X. And you should have an idea of how this is connected with the slope of the tangent line.
Title:
Exponential Function - Differential Equations in Action
Video Language:
English
Team: Udacity
Project:
CS222 - Differential Equations
Duration:
01:21 Udacity Robot edited English subtitles for Exponential Function - Differential Equations in Action sp1 added a translation

# English subtitles

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