help with derivative of a^x

[synx]

I have to prove the derivative of a^x is a^xln(a) using just the basic definition of derivs.
I get h->0 lim a^x * (a^h - 1) / h , so i see how you get a^x, but can someone explain to me how ln(x) comes from (a^h - 1) / h ? Thanks.

 

[Gene]

Start with
y=a^x
ln(y)=x*ln(a)
dy/y=ln(a)dx
dy/dx=y*ln(a) = a^x*ln(a)