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Derivative of a^x.
I am studying the attached image:
Attachment 29733
I find myself wondering is it:
$\displaystyle m(a)=\lim \Delta x\rightarrow 0\frac{a^\Delta^x1}{\Delta x}$
or is it:
$\displaystyle m(a)=a^x\lim \Delta x\rightarrow 0\frac{a^\Delta^x1}{\Delta x}$
Thanks in advance...

Re: Derivative of a^x.

Re: Derivative of a^x.
Why then is it said:
$\displaystyle m(a)=\frac{d}{dx}a^x ...at... x=0$
it is confusing me if m(a) is the first one I posted. Clearly before they said:
$\displaystyle m(a)=\frac{d}{dx}a^x=m(a)a^x$
Thanks in advance...

Re: Derivative of a^x.
OK. That would mean a^x is one at x = 0. I think I get it now.

Re: Derivative of a^x.