Warning: Derivative of 3²

That's right, $3^x$ is just a function of the variable $x$. If you prefer, we can emphasize that it's a function of $x$ by saying something like "$3^x$ refers to the function $f(x)=3^x$".

Exactly! As we saw earlier, when we say, "take the derivative $3^2$," we mean we are taking the derivative of the function $f(x) = 3^2$, which is just the derivative of $f(x)=9$ which is (always, for any input $x$) $0$.

As you just saw, this distinction is important to make. Hope you found this interesting and insightful!

Although $3^2$ does follow the mold for an exponent, the general rule for differentiating exponents with variables does not apply. Although

$\frac{d}{dx}3^x = \ln 3 \cdot 3^x$,

we cannot plug in values of $x$. This would imply that

$\frac{d}{dx}3^2 = \ln 3 \cdot 3^2$

Realize that $3^2$ is a constant because it does not contain any variables. Like all other constants, the derivative of $3^2$ is $0$ (rewrite $3^2$ as $9$ if this still confuses you).

A derivative is not a function from the reals to the reals, but rather a function taking functions from the reals to the reals to other functions taking the reals to the reals. For more detail, see Derivative as a Function.