# Math Help - Exponential functions: a function of themselves

1. ## Exponential functions: a function of themselves

Hey,

I've read on James Stewart's Calculus (7th edition, I believe) that exponential functions are a function of themselves.

Just like: Y= f(Y)

how this can be? I mean, if we write things like that, we are supposing that Y is a function of Y at the current period, which is not true, exponential functions are a function of their past periods, in other words, Y at (t+1) is a function of Y at (t)

2. ## Re: Exponential functions: a function of themselves

I don't get what you're saying...the derivative of the exponential function is in terms of the original function, that is

$\frac{d}{dx} a^x = a^x \ln a$. In particular, when a = e,

$\frac{d}{dx} e^x = e^x$