Differentiate a^x w.r.t. x, where a is a positive constant.

The correct answer is Option (3) → $a^x \ln a$ ##

Let $y = a^x$. Then

$\log y = x \log a$

Differentiating both sides w.r.t. $x$, we have

$\frac{1}{y} \frac{dy}{dx} = \log a$

or $\frac{dy}{dx} = y \log a$

Thus $\frac{d}{dx}(a^x) = a^x \log a$