# Derivative of a^x.

• Nov 14th 2013, 08:13 PM
sepoto
Derivative of a^x.
I am studying the attached image:
Attachment 29733

I find myself wondering is it:
$m(a)=\lim \Delta x\rightarrow 0\frac{a^\Delta^x-1}{\Delta x}$

or is it:

$m(a)=a^x\lim \Delta x\rightarrow 0\frac{a^\Delta^x-1}{\Delta x}$

• Nov 14th 2013, 08:20 PM
SlipEternal
Re: Derivative of a^x.
It is the first one.
• Nov 14th 2013, 08:30 PM
sepoto
Re: Derivative of a^x.
Why then is it said:

$m(a)=\frac{d}{dx}a^x ...at... x=0$

it is confusing me if m(a) is the first one I posted. Clearly before they said:

$m(a)=\frac{d}{dx}a^x=m(a)a^x$