# Derivation of the exponential distribution - that infinitesimal!

1. Jan 20, 2014

### thomas49th

Hello,

I've been looking at the derivation of the exponential function, here
http://www.statlect.com/ucdexp1.htm
amongst other places, but I don't get how, why or what the o(delta t) really does. How does it help?

It's really confusing me, and all the literature I've looked at just seems to quickly dance over it

Thanks

2. Jan 20, 2014

### Staff: Mentor

$o(\Delta t)$ contains all small terms the derivation does not want to (and does not have to) care about. Something like $(\Delta t)^2$, $(\Delta t)^3$ and so on.

Little-o notation

3. Jan 20, 2014

### thomas49th

why do those terms exist? was there some kind of taylor expansion?

4. Jan 20, 2014

### Staff: Mentor

Exactly. It is a taylor approximation to first order (linear in Δt) and higher orders are neglected.

5. Jan 20, 2014

### thomas49th

what the taylor expansion of? e^x ?

6. Jan 21, 2014

### Staff: Mentor

Should be $e^x - e^{x+Δt}$ with some prefactors I did not check.