The problem states that $f(x) = \ln(x+1)$. We are asked to find some information about the function. However, the problem is incomplete. I assume we are supposed to find the derivative of $f(x)$.

1. Problem Description

The problem states that $f(x) = \ln(x+1)$. We are asked to find some information about the function. However, the problem is incomplete. I assume we are supposed to find the derivative of $f(x)$.

2. Solution Steps

To find the derivative of $f(x) = \ln(x+1)$, we can use the chain rule.

The chain rule states that if we have a composite function $f(g(x))$, then its derivative is $f'(g(x)) \cdot g'(x)$.

In this case, let $g(x) = x+1$. Then $f(g(x)) = \ln(g(x)) = \ln(x+1)$.

The derivative of $\ln(x)$ is $\frac{1}{x}$.

So, $f'(g(x)) = \frac{1}{g(x)} = \frac{1}{x+1}$.

The derivative of $g(x) = x+1$ is $g'(x) = 1$.

Therefore, the derivative of $f(x) = \ln(x+1)$ is $f'(x) = \frac{1}{x+1} \cdot 1 = \frac{1}{x+1}$.

3. Final Answer

$f'(x) = \frac{1}{x+1}$