1. The problem is to find the derivative of $\cos(ax)$ with respect to $x$. 2. The formula for the derivative of cosine function is: $$\frac{d}{dx}(\cos u) = -\sin u \cdot \frac{du}{dx}$$ where $u$ is a function of $x$. 3. Here, $u = ax$, so $\frac{du}{dx} = a$. 4. Applying the chain rule: $$\frac{d}{dx}(\cos(ax)) = -\sin(ax) \cdot a = -a \sin(ax)$$. 5. Therefore, the derivative of $\cos(ax)$ is $$-a \sin(ax)$$. This matches the given formula in the problem statement.