Partial Derivative Visualization: Tangent Plane and Directional Slopes on a Surf

① This example demonstrates the geometric meaning of partial derivatives of a multivariable function at a point by showing a 3D surface with its tangent plane and directional line segments. ② The core mathematical concept is the partial derivative, representing the rate of change with respect to one variable while holding others fixed, along with tangent planes and directional derivatives. ③ Construction highlights: using GeoGebra commands such as Derivative to compute partial derivatives, Plane to create the tangent plane, Segment and Line for direction indicators, and Textfield/InputBox for interactive input; objects include surface f, partial derivatives dfx and dfy, point P, tangent plane XYP, and multiple text labels. ④ Suitable for university-level calculus or multivariable calculus courses, as well as advanced high school enrichment or teacher demonstrations, to bridge geometric intuition with formal definitions.