Derivative of General Exponential Function

Corollary
Let $a \in \R: a > 0$.

Let $a^x$ be $a$ to the power of $x$.

Then:
 * $D_x \left({a^x}\right) = a^x \ln a$

Proof
From the definition of Power to Real Number:
 * $a^x = e^{x \ln a}$

Thus from Corollary 1:
 * $D_x \left({a^x}\right) = D_x \left({e^{x \ln a}}\right) = \ln a e^{x \ln a} = a^x \ln a$