Visualizing the Derivative of f(x)=ln(x) via Tangent Slope

This example demonstrates how to visualize the derivative of f(x)=ln(x) by constructing the tangent line at a chosen point and using its slope as the geometric meaning of the derivative. Key concepts include logarithmic functions, the derivative as the instantaneous rate of change, and the “derivative equals tangent slope” interpretation. In GeoGebra, you define the function f(x) (the graph of ln(x)), pick a point A on the curve, construct the tangent g at A, and then compute the tangent slope m using the Slope command. A related point P is used to mark or display the slope/tangent information clearly, making the relationship between the curve’s local behavior and the derivative visually explicit. Suitable for calculus introduction, learning derivative intuition, and classroom demonstrations for students building graph-based understanding of derivatives.