First principles differentiation question

[tunabeast]

Homework Statement

Obtain the derivative of e^{2x} from first principles.

Homework Equations

The Attempt at a Solution

I am upto the point where i have e^{2x}(\frac{e^{2h}-1}{h}) Where LIM h->0.

I just don't see how 2 is obtained from what's in the ().

 

[HallsofIvy]

\frac{e^{2h}-1}{h}= 2\frac{e^{2h}-1}{2h}= 2\frac{e^u -1}{u}
if you let u= 2x.

Now, do you know what the limit, as u goes to 0 of
\frac{e^u- 1}{u}
is?

 

[tunabeast]

It tends to 1? I think i understand this now, thanks very much for your help.