Visualizing the Product Rule: Derivative of a Product of Functions

① This GeoGebra example dynamically illustrates the Product Rule in calculus, showing how the derivative of the product h(x)=f(x)g(x) is composed from the functions f, g and their derivatives. ② Core mathematical concepts include derivatives, the product rule, function graphs, tangent slopes, and differential approximations, focusing on the rate of change of a product. ③ Construction highlights: from the summary, the example uses the Polygon command to build multiple polygonal regions (A, B, C, D, etc.), defines function objects (f, g, a, c, d, etc.), text objects (text1 to text5), a button (button1), sliders (n, dx), and points (E, F, G, H, I) to mark key positions. It likely visualizes the product's infinitesimal change via rectangular areas or increments dx, thereby deriving the product rule geometrically. ④ Suitable for high school to early college students learning calculus, ideal for classroom demonstrations or self-study, helping to grasp the essence of derivative rules, and useful for teachers creating interactive materials.