1. **State the problem:** Simplify the expression and find the derivative where applicable: $2\sqrt{x}3 - 5 - \frac{d}{dx} 11 \sqrt{x} 12 - 1$. 2. **Rewrite the expression clearly:** $$2 \cdot 3 \sqrt{x} - 5 - \frac{d}{dx} (11 \cdot 12 \sqrt{x}) - 1$$ 3. **Simplify constants:** $$6 \sqrt{x} - 5 - \frac{d}{dx} (132 \sqrt{x}) - 1$$ 4. **Recall the derivative rule for $\sqrt{x}$:** $$\frac{d}{dx} \sqrt{x} = \frac{1}{2 \sqrt{x}}$$ 5. **Apply the derivative:** $$\frac{d}{dx} (132 \sqrt{x}) = 132 \cdot \frac{1}{2 \sqrt{x}} = \frac{132}{2 \sqrt{x}}$$ 6. **Simplify the derivative:** $$\frac{132}{2 \sqrt{x}} = \frac{\cancel{132}}{\cancel{2} \sqrt{x}} = \frac{66}{\sqrt{x}}$$ 7. **Substitute back into the expression:** $$6 \sqrt{x} - 5 - \frac{66}{\sqrt{x}} - 1$$ 8. **Combine like terms:** $$6 \sqrt{x} - 6 - \frac{66}{\sqrt{x}}$$ 9. **Final simplified expression:** $$6 \sqrt{x} - 6 - \frac{66}{\sqrt{x}}$$