Visualizing the Derivative of the Inverse

① This interactive GeoGebra example visualizes the geometric relationship between a function and its inverse, demonstrating that the derivative of the inverse at a point equals the reciprocal of the derivative of the original function at the corresponding point. ② Core mathematical concepts include inverse functions, derivatives, tangent line slopes, symmetry about the line y=x, and the trigonometric connection between slope and angle. ③ Construction details: Based on the summary, the construction uses GeoGebra commands such as Point, Locus, Tangent, Slope, Intersect, and Line, creating functions f and g (mutually inverse), points A and B, a locus loc1, tangent lines h and i, slope objects m and m_1, and multiple text labels (text1, text2, text3) to display numerical relationships. ④ Suitable for advanced high school or introductory college calculus students, this example helps learners grasp the geometric meaning of the inverse function derivative formula, and serves as an effective classroom demonstration or self-guided exploration tool.