## ← Exponential Function - Differential Equations in Action

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

1. Euler's number and the exponential function based on that number are of vital importance in the theory of differential equations.
2. Whenever we are dealing with exponential growth or exponential decay, and whenever we deal with oscillations,
3. Euler's number plays a big role. This is a brief and informed introduction to that topic, for which we need a minimum
4. amount of prerequisites. In particular, you should know that five to the first power equals five.
5. Five to the zeroth power equals one. Five to the minus second power equals one over 25.
6. Five to the power of one half equals the square root of five.
7. Five to the third power times five to the fourth power equals five to the power of three plus four--seven.
8. And five to the third power to the fourth power equals five to the power of 12--three times four.
9. This is what you need to know about powers of numbers.
10. In addition, you should have an idea about derivatives in this D, DX notation--for instance, the derivate of X squared
11. with respect to X equals 2X. And you should have an idea of how this is connected with the slope of the tangent line.