1. The problem is to find the partial derivative of $\cos x$ with respect to $x$. 2. The formula for the derivative of $\cos x$ is $\frac{d}{dx} \cos x = -\sin x$. 3. Since $\cos x$ is a function of $x$ only, the partial derivative with respect to $x$ is the same as the ordinary derivative. 4. Therefore, $\frac{\partial}{\partial x} \cos x = -\sin x$. 5. This means the rate of change of $\cos x$ with respect to $x$ is $-\sin x$. Final answer: $$\frac{\partial}{\partial x} \cos x = -\sin x$$