1. The problem asks to find the derivative of $\cos(ax)$ with respect to $x$. 2. According to the derivative formula given: $$\frac{d}{dx}(\cos ax) = -a \sin ax$$ 3. Here, $a$ is a constant and $x$ is the variable. 4. The derivative of $\cos(ax)$ is calculated by multiplying $-a$ by $\sin(ax)$. 5. So, the derivative is $$-a \sin(ax)$$. This means if you have a function $f(x) = \cos(ax)$, its rate of change at any point $x$ is given by $f'(x) = -a \sin(ax)$. Final answer: $$\frac{d}{dx}(\cos ax) = -a \sin ax$$