GeoGebra Visualization of the Power Rule for x^n Derivatives

This example demonstrates—through a dynamic GeoGebra construction—how the derivative of a power function x^n follows the power rule, making the transformation from the original function to its derivative visually traceable. Key math concepts include power-function differentiation, the meaning of derivatives as local rate of change, parameter dependence on the exponent n, and building a clear correspondence between displayed expressions and geometric quantities. In the construction, LaTeX is used to typeset the key formulas and labels; objects a, h, k, b, n, g, f represent parameters and function/auxiliary elements; multiple text objects (text1–text4) annotate variables and the resulting derivative statement; reflect is used to introduce a symmetry/reflective geometric relationship that highlights the “matching” quantities between the setup and the rule; intermediate object p and the additional text3 help connect the current configuration (selected n and related elements) to the final derivative expression. Suitable for calculus lessons (upper secondary to first-year university), especially for teaching derivative rules and validating the power rule via visualization.