Please ignore this unless you're really interested, I'm just gonna post the solution of this up - at least it shows a more interesting function I suppose.
You need to use the fact that:
[math]e = \lim_{n\to\infty}\left(1 + \frac{1}{n}\right)^n[/math].
Take f(x) = ex. Then you get that:
[math]f'(x) = e^x \lim_{h\to 0} \left( \frac{e^h - 1}{h} \right)[/math]
Notice that from the first equation, by putting n = 1/h,
[math]e = \lim_{h\to 0} (1+h)^{\frac{1}{h}}[/math].
Now we get that [math] e^h = \lim_{h\to 0} (1+h)[/math]
So by bunging this into our original equation, we have that our other bit of the limit tends to 1, which means f'(x) = ex.