1. **Problem:** Find the derivative of the function $y = 2 \ln x$. 2. **Formula:** The derivative of $\ln x$ with respect to $x$ is $\frac{1}{x}$. 3. **Step-by-step solution:** 1. The function is $y = 2 \ln x$. 2. Since 2 is a constant multiplier, use the constant multiple rule: $\frac{d}{dx}[c f(x)] = c \frac{d}{dx} f(x)$. 3. Differentiate $\ln x$: $\frac{d}{dx} \ln x = \frac{1}{x}$. 4. Multiply by the constant 2: $\frac{dy}{dx} = 2 \cdot \frac{1}{x} = \frac{2}{x}$. 4. **Answer:** $$\boxed{\frac{dy}{dx} = \frac{2}{x}}$$ This means the rate of change of $y$ with respect to $x$ is $\frac{2}{x}$.