Function and Its Derivative Visualization

① This GeoGebra example dynamically displays a function f and its derivative df, illustrating the relationship between the rate of change and the slope of the curve. ② Core mathematical concepts include derivatives, tangent slopes, monotonicity, and fundamental calculus ideas, covering linear, logarithmic, and trigonometric functions. ③ Construction highlights: the Derivative command is used to compute df from f, and both graphs are plotted simultaneously; by adjusting parameters or sliders, users can observe how the derivative graph changes, reinforcing the geometric interpretation of the derivative as the slope of the tangent line at each point. ④ Suitable for high school to early college calculus courses, this tool aids in teaching the definition and geometric meaning of derivatives, as well as differentiation rules for common functions, and serves as an interactive exploration resource for students.