1. **Problem:** Find the derivative of $y = \sin^2 3x - 5$. 2. **Formula:** Use the chain rule and power rule. If $y = (\sin u)^2$, then $\frac{dy}{dx} = 2 \sin u \cdot \cos u \cdot \frac{du}{dx}$. 3. **Step-by-step:** - Let $u = 3x$, so $\frac{du}{dx} = 3$. - Then $y = (\sin 3x)^2 - 5$. - Derivative: $\frac{dy}{dx} = 2 \sin 3x \cdot \cos 3x \cdot 3 = 6 \sin 3x \cos 3x$. 4. **Simplify:** Using the double angle identity $\sin 2\theta = 2 \sin \theta \cos \theta$, we get $$\frac{dy}{dx} = 3 \sin 6x$$ **Final answer:** $$\boxed{\frac{dy}{dx} = 3 \sin 6x}$$