1. **State the problem:** Differentiate the function $f(x) = \sin x$ with respect to $x$. 2. **Recall the differentiation rule:** The derivative of $\sin x$ with respect to $x$ is $\cos x$. 3. **Apply the rule:** $$\frac{d}{dx}(\sin x) = \cos x$$ 4. **Interpretation:** This means the rate of change of the sine function at any point $x$ is given by the cosine of $x$. **Final answer:** $$\frac{d}{dx}(\sin x) = \cos x$$