Partial Derivatives: Visualizing Tangent Slopes on a Surface

This GeoGebra example dynamically illustrates the geometric meaning of partial derivatives for a two-variable function, showing the slopes of tangent lines along the x- and y-axes at a chosen point. Core concepts include partial derivatives, tangent planes, directional derivatives, and local linear approximation of surfaces. Construction details: the IntersectPath command creates intersection curves between the surface and vertical planes, Vector draws direction vectors, and Line constructs tangent lines. Sliders control the point (x0, y0), updating the displayed values of PartialX and PartialY in real time. Suitable for university-level calculus or multivariable calculus courses, as well as advanced high school enrichment, this tool helps students intuitively grasp how partial derivatives measure the rate of change along coordinate axes.