Derivative of Vector-Valued Function: Geometric Meaning of Parametric Curve Tang

This example demonstrates the geometric interpretation of the derivative of a vector-valued function with respect to its parameter. Using the CurveCartesian command to construct parametric curves, Vector commands to represent position and velocity vectors, Tangent to draw tangents, and Translate for vector translation. The core mathematical concept is that the derivative of a vector-valued function (velocity vector) indicates the tangent direction of the curve, while its magnitude reflects the rate of change at that point. The construction uses a slider parameter t to control point P moving along the curve, simultaneously displaying the tangent and velocity vector v at P, intuitively showing the instantaneous rate of change meaning of derivatives. Suitable for high school mathematics extension courses or university calculus courses covering parametric curves and vector analysis.