e (2.71828)

No, this is not a post for luvved-up early 90s teenagers.

e is a bizarrely cool number, sometimes known as the natural logarithm.

Like π it is an irrational number - ie it cannot be expressed exactly as the ratio of two whole numbers (and thus as a fraction).

How do we get it then?

Imagine an exponential curve. A curve that is n^x. Say, y= 3^x.

As usual, the gradient will generally differ as x differs.

Is there a curve which has a gradient of 1, where x=0? There is, and, coolly, this curve has a gradient of 1 where x=0 and ALSO passes through y=1, ie the value of the function is 1.

This curve is y = e ^x. It's not just at y=1 where the value of the function equals the gradient, it's every point on the curve.

As you can imagine, that makes differentiating with e easy...

There is an excellent page here which shows you some interesting examples of e in action.