Sketching Derivatives: Interactive Function and Its Derivative Graph

① This GeoGebra example demonstrates how to sketch the derivative f' of a given function f interactively, with an input box allowing users to modify the function and instantly see the resulting derivative graph. ② Core mathematical concepts include the geometric meaning of derivatives (slope of tangent lines), the relationship between a function and its derivative, and using derivatives to analyze monotonicity and extrema. ③ Construction highlights: The Derivative command generates the derivative function, while Textfield and InputBox1 provide an editable input field; when the user types a new function, both f and f' update automatically, with parameter a possibly controlling display range or a specific point. ④ Suitable for high school to early college calculus instruction, ideal for classroom demonstrations of derivative concepts, student exploration of derivative shapes for various functions, or as an interactive homework tool.