Originally Posted by

**Boris B** I finally figured out in the assignment I'm doing that one of the variables, known as e, is *the* e. I.e., it's not actually a variable.

I gather (but can't prove) that of the properties of e is that"

$\displaystyle f(x) = e^x $

$\displaystyle f'(x) = e^x$

Having forgotten that e is not just a regular variable, I decided to take the derivative the old-fashioned way:

$\displaystyle f(x) = e^x $

$\displaystyle f'(x) = x \cdot e^{x-1}$

This leads me astray. Plugging in x=2, I find that ordinary derivation gives me:

$\displaystyle f(2) = e^2 $

$\displaystyle f'(2) = 2 \cdot e^{2-1} = 2e$

and I'm pretty sure

$\displaystyle e^2 = 2e$

only when e=2. And because this is *the* e, it doesn't equal 2!

I can solve the problem now, only I have somewhat less faith in my new ability (?) to take a basic derivative. Is it just that ordinary derivation doesn't work with transcendental / irrational numbers, or did I derive wrong?