Parametric Derivatives: Visualizing Tangent Vectors

① This example demonstrates the geometric meaning of derivatives for parametric curves by showing a dynamic point and its tangent vector. ② Core math concepts include parametric equations, derivatives (dy/dx in terms of dx/dt and dy/dt), vectors, and tangent directions. ③ Construction highlights: uses GeoGebra commands CurveCartesian to plot the parametric curve, defines parameter t and functions f, g; uses Vector to construct tangent vectors u, v, w, with points A, B, C, D and slider a for dynamic control; text objects text1 to text6 display derivative expressions and values. ④ Suitable for high school to early college calculus or analytic geometry courses, helping students grasp the computation and visual intuition of parametric differentiation, and useful for classroom demonstrations or self-study.