Find the derivative of the function $y={\left(2x\right)}^{3\sqrt{x-2}}$.

• A. ${\left(2x\right)}^{3\sqrt{x-2}}(\frac{3\ln 2x}{2\sqrt{x-2}}-\frac{3\sqrt{x-2}}{x})$
• B. ${\left(2x\right)}^{3\sqrt{x-2}}(\frac{3\ln 2x}{2\sqrt{x-2}}+\frac{3\sqrt{x-2}}{x})$
• C. ${\left(2x\right)}^{3\sqrt{x-2}}(\frac{3\ln 2x}{2\sqrt{x-2}}+\frac{3\sqrt{x-2}}{2x})$
• D. ${\left(2x\right)}^{3\sqrt{x-2}}\ln 2$