Geometric Meaning of Derivative for f(x)=ln(x)

This example demonstrates the geometric meaning and calculation process of the derivative for the natural logarithm function f(x)=ln(x). Through dynamic visualization, students can intuitively understand that the derivative represents the slope of the tangent line at any point on the function. Core mathematical concepts include: derivative formula for logarithmic functions, geometric interpretation of derivative (tangent slope), and the limit definition. Construction details: This example uses GeoGebra's Tangent command to draw the tangent line at point P on the function curve, the Slope command to calculate the tangent slope, and LaTeX commands to dynamically display the derivative formula and tangent equation. Objects include: function f(x)=ln(x), moving point P, tangent line g, slope value m, and corresponding text labels. Suitable for high school mathematics (introduction to derivatives) or university calculus courses, can be used for classroom teaching demonstration or student self-exploration of derivative concepts.