Real exponential function/Base/Derivative/Fact

The exponential function

$\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto a^{x},$

with base ${}a>0$,

is

differentiable with

${}{\left(a^{x}\right)}'={\left(\ln a\right)}a^{x}\,.$

Proof, Write another proof