1. **Problem:** Find the derivative of the function $y = 2 \ln x$. 2. **Formula and rules:** The derivative of $\ln x$ with respect to $x$ is $\frac{1}{x}$ for $x > 0$. 3. **Apply the constant multiple rule:** Since $y = 2 \ln x$, the derivative is $$y' = 2 \cdot \frac{d}{dx} (\ln x) = 2 \cdot \frac{1}{x} = \frac{2}{x}.$$ 4. **Explanation:** The constant multiple rule states that the derivative of a constant times a function is the constant times the derivative of the function. Here, the constant is 2 and the function is $\ln x$. 5. **Final answer:** $$\boxed{\frac{dy}{dx} = \frac{2}{x}}$$