Find the derivative of e^{2x} by the first principle.

I want to know to things

The first one is, why is the number 2 in red coming up there? It doesn't make sense to me.

The second is, for the right side of the function (e^{h}-1)/2h is the limit going to be 0 or 1, and why?

Please see the picture below where I got confused.

Thanks

**Transcribed image text: **

2x+2h 2x e е e ho f(es. et f(x) = Lim f(x) lim ele 1) f(x) = et lim en h f(x) = (2x lim 2 (e"..) the limit h e-1 h-so hose 12h will be solo? why is this 2 there? f'(x) = 2 e2²