# 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

## 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 =

`a`, 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

^{x}`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.