The problem asks us to determine the derivative of the function $y = \cos x$.

1. Problem Description

The problem asks us to determine the derivative of the function $y = \cos x$.

2. Solution Steps

The derivative of the cosine function is the negative sine function. This is a standard result in calculus.

$\frac{d}{dx} \cos x = -\sin x$

Therefore, the derivative of $y = \cos x$ with respect to $x$ is:

$\frac{dy}{dx} = -\sin x$

3. Final Answer

$-\sin x$