Copy of 3-Way Color-Changing Derivative Grapher

① This interactive example demonstrates a three-way color-changing derivative grapher that dynamically displays a function, its derivative, and the slope of the tangent line, making the geometric relationship between a function and its derivative visually intuitive. ② Core mathematical concepts include derivatives, tangent slopes, function graphs, parametric curves, and slope-field ideas from differential equations, with examples involving sine functions. ③ Construction highlights: using GeoGebra commands such as Tangent, Slope, Textfield, Intersect, Circle, and Vector, the applet builds objects including function f, its derivative f', point A, slope m, input boxes InputBox1/2, buttons button1-4, and related elements, enabling interactive input and real-time updates. ④ Suitable for high school to college-level calculus instruction, this tool helps students grasp the geometric meaning of derivatives, tangent slope computation, and visualization of rates of change, and is ideal for classroom demonstrations or self-directed exploration.