1. **Problem:** Find the derivative of the function $f(x)=\ln x$. 2. **Recall the derivative rule:** The derivative of the natural logarithm function $\ln x$ is given by $$\frac{d}{dx} \ln x = \frac{1}{x}.$$ 3. **Explanation:** This comes from the fact that $\ln x$ is the inverse function of the exponential function $e^x$. Using implicit differentiation or the chain rule proves this result. 4. **Final answer:** $$\boxed{\frac{d}{dx} \ln x = \frac{1}{x}}.$$