1. **State the problem:** We need to find the 2025th derivative of the function $g(x) = \cos(x)$. 2. **Recall the derivatives of cosine:** The derivatives cycle every 4 steps: $g'(x) = -\sin(x)$ $g''(x) = -\cos(x)$ $g^{(3)}(x) = \sin(x)$ $g^{(4)}(x) = \cos(x)$ (back to the original function) 3. **Determine the remainder when 2025 is divided by 4:** $$2025 \div 4 = 506 \text{ remainder } 1$$ This means the 2025th derivative has the same form as the first derivative in the cycle. 4. **Identify the 1st derivative function:** $g'(x) = -\sin(x)$ 5. **Conclusion:** The 2025th derivative is $g^{(2025)}(x) = -\sin(x)$, which corresponds to option B. **Final answer:** B) $-\sin(x)$