1. **State the problem:** Find the derivative of the function $f(x) = \ln x$. 2. **Recall the formula:** The derivative of the natural logarithm function $\ln x$ with respect to $x$ is given by $$\frac{d}{dx} \ln x = \frac{1}{x}$$ 3. **Explanation:** This formula holds for $x > 0$ because the natural logarithm is only defined for positive real numbers. 4. **Intermediate work:** Since $f(x) = \ln x$, applying the formula directly gives $$f'(x) = \frac{1}{x}$$ 5. **Final answer:** The derivative of $\ln x$ is $$\boxed{\frac{1}{x}}$$ This means the rate of change of $\ln x$ at any point $x$ is the reciprocal of $x$.