This proof is similar to ex. In fact, e can be plugged in for a, and we would get the same answer because ln(e) = 1.
Rewrite ax as an exponent of eln
Use Chain Rule and substitute u for xlna
Cancel out dx over dx, and substitute back in for u
Bring down the ax
Here is a graph of f(x) = .5x and f(x) = 2x and their derivatives.