1. The problem is to find the derivative of the function $\cos x$ with respect to $x$. 2. The formula for the derivative of the cosine function is: $$\frac{d}{dx}(\cos x) = -\sin x$$ This is a standard derivative rule in calculus. 3. Applying the formula directly: $$\frac{d}{dx}(\cos x) = -\sin x$$ 4. Explanation: The cosine function decreases as $x$ increases, and its rate of change is given by the negative sine of $x$. This means the slope of the tangent line to the curve $y=\cos x$ at any point $x$ is $-\sin x$. Final answer: $$\frac{d}{dx}(\cos x) = -\sin x$$