I like dy/dx notation and substitution whenever the chain rule comes up.

$y = a^x = e^{xln(a)}.$

$u = xln(a) \implies \dfrac{du}{dx} = ln(a).$

$And\ u = x * ln(a) \implies y = e^u \implies \dfrac{dy}{du} = e^u = e^{xln(a)} = a^x \implies \dfrac{dy}{dx} = \dfrac{dy}{du} * \dfrac{du}{dx} \implies$

$\dfrac{dy}{dx} = a^x * ln(a).$