1. The problem is to find the derivative of the function $g(x) = \ln(7x + 2)$.\n\n2. The formula for the derivative of a natural logarithm function $\ln(f(x))$ is given by:\n$$\frac{d}{dx} \ln(f(x)) = \frac{f'(x)}{f(x)}$$\nwhere $f(x)$ is a differentiable function and $f'(x)$ is its derivative.\n\n3. In this problem, $f(x) = 7x + 2$. We need to find $f'(x)$, the derivative of $7x + 2$.\n\n4. The derivative of $7x + 2$ with respect to $x$ is:\n$$f'(x) = \frac{d}{dx}(7x + 2) = 7$$\n\n5. Applying the formula for the derivative of the logarithm, we get:\n$$g'(x) = \frac{f'(x)}{f(x)} = \frac{7}{7x + 2}$$\n\n6. Therefore, the derivative of $g(x) = \ln(7x + 2)$ is:\n$$g'(x) = \frac{7}{7x + 2}$$\n\nThis is the correct derivative, and the answer is not just 7 but the fraction $\frac{7}{7x + 2}$.