1. The problem is to find the derivative of the natural logarithm of a function $f(x)$ with respect to $x$. 2. Recall the chain rule for derivatives: if $y = \ln(f(x))$, then the derivative $\frac{dy}{dx}$ is given by $$\frac{dy}{dx} = \frac{1}{f(x)} \cdot f'(x)$$ where $f'(x)$ is the derivative of $f(x)$. 3. This means the derivative of $\ln(f(x))$ is the derivative of the inside function $f(x)$ divided by $f(x)$ itself. 4. Therefore, the final answer is: $$\frac{d}{dx} \ln(f(x)) = \frac{f'(x)}{f(x)}$$