Differentiating exponentials 1, the Euler constant e

This applet shows the importance of the Euler Number e in relation to differentiating exponential functions.

Author and programmer: Ron Barrow

UK Years 12-13, KS5, Core 3 (C3) GCE Mathematics, Algebra and Functions
US - Grades 11 - 12


Instructions below    See also:    Exponential Functions    Differentiating polynomials    Integrating polynomials

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How to Use this Applet

The applet on this page has a simple aim - to introduce the number e, sometimes called the Euler Number or the base of Natural or Naperian logarithms.
The black graph is y = ax, and the blue one is its derivative or gradient graph. Notice how they have the same kind of shape. There is one value of the base a where the graph and the gradient graph are the same. By using the slider to change the value of a, you notice that when a is about 2.72, the graphs coincide. This number is e, although in truth it is an irrational number, 2.71828....
This number, e, is one of the most important numbers in mathematics, and you'll meet it many times in the future.