1. Stating the problem: We want to find the derivative of the function $y = \sin x$.\n\n2. Recall the derivative rule: The derivative of $\sin x$ with respect to $x$ is $\cos x$.\n\n3. Writing the derivative: $$\frac{dy}{dx} = \cos x$$\n\n4. Explanation: This means that the rate of change or slope of the sine function at any point $x$ is given by the cosine of $x$.\n\nFinal answer: The derivative of $\sin x$ is $\cos x$.