1. **Problem Statement:** Differentiate the function $\sin^2 u$, which means find $\frac{d}{du}(\sin^2 u)$. 2. **Formula Used:** Use the chain rule for differentiation: if $y = [f(u)]^2$, then $\frac{dy}{du} = 2 f(u) \cdot f'(u)$. 3. **Apply the Chain Rule:** Here, $f(u) = \sin u$, so $f'(u) = \cos u$. 4. **Differentiate:** $$\frac{d}{du}(\sin^2 u) = 2 \sin u \cdot \cos u$$ 5. **Final Answer:** $$\frac{d}{du}(\sin^2 u) = 2 \sin u \cos u$$ This is the derivative of $\sin^2 u$ with respect to $u$.