To solve this problem, we need to find the derivative of the given function:

$g(x) = \ln(6x + 5)$

Steps to Solve:

1. Derivative of the natural logarithmic function: The derivative of $\ln(u)$ is given by: $\frac{d}{dx} \ln(u) = \frac{1}{u} \cdot \frac{du}{dx}$

2. Apply the formula: Here, $u = 6x + 5$, so: $\frac{du}{dx} = \frac{d}{dx}(6x + 5) = 6$

   Substituting into the formula: $g'(x) = \frac{1}{6x + 5} \cdot 6$

3. Simplify: $g'(x) = \frac{6}{6x + 5}$

Correct Answer:

$\boxed{g'(x) = \frac{6}{6x + 5}}$

This matches the first option.

Let me know if you want further explanation or have questions! Here are some related questions:

1. How do we apply the chain rule in derivative problems?
2. What is the derivative of other logarithmic functions like $\ln(ax + b)$?
3. Can this derivative be used in optimization problems? If yes, how?
4. What happens to the derivative when the function is shifted or scaled?
5. How do logarithmic derivatives differ from power rule derivatives?

Tip: Always identify inner and outer functions when using the chain rule!