1. The problem asks to find the derivative of $\sin(ax)$ with respect to $x$. 2. According to the derivative formulas, the derivative of $\sin(ax)$ is given by: $$\frac{d}{dx} (\sin(ax)) = a \cos(ax)$$ 3. Here, $a$ is a constant multiplier inside the sine function, and $x$ is the variable. 4. The formula uses the chain rule: the derivative of $\sin(u)$ is $\cos(u)$ times the derivative of $u$, where $u = ax$. 5. Since $\frac{d}{dx}(ax) = a$, multiply $\cos(ax)$ by $a$. 6. Therefore, the derivative is: $$\boxed{a \cos(ax)}$$ This is the final answer.