**Solution.**Let F(x) = \ln(x+1), f(u) = \ln(u) and g(x) = x + 1. Then we will use the chain rule:

\begin{align*} F'(x) = f'(g(x))g'(x). \end{align*}

\begin{align*} f'(u) = \frac{1}{u} \quad \text{and} \quad g'(x) = 1. \end{align*}

\begin{align*} F'(x) &= f'(g(x))g'(x) \\ &= \frac{1}{x + 1} \cdot 1 \\ &= \frac{1}{x + 1}. \end{align*}