Derivatives of x^n: From Function to Slope

This example visualizes how the derivative of the power function y = x^n changes with x, showing an explicit geometric link between the original graph and the derivative-related behavior (e.g., how slopes evolve across the domain). Key concepts include the power rule for derivatives (d/dx(x^n)=n·x^{n-1}), the interpretation of a derivative as a rate of change, and graph transformations such as scaling/dilation effects. In GeoGebra, construction is supported by LaTeX typesetting for formulas and labels; objects include parameters like a, h, k, b, n, g, the function object f, and multiple text items (text1–text4) to guide interpretation. The scene also uses objects such as reflect and p to perform or illustrate geometric positioning/symmetry aspects that help relate derivative features back to the original function. Suitable for calculus introduction, derivative teaching, and graph-based understanding for high school advanced or early college learners.