Exploring the Derivative as a Function

① This GeoGebra example dynamically visualizes how the derivative of a function forms a new graph while displaying the original function’s tangent line and its slope at any point. ② Key mathematical concepts include the definition of the derivative, the geometric interpretation of the derivative function, tangent line equations, and the relationship between slope and derivative. ③ The construction uses GeoGebra commands such as Derivative, Point, Tangent, Slope, Segment, and interactive controls like Textfield, InputBox1, and InputBox2 to enable user input and real‑time manipulation. ④ Designed for high‑school to early university students, it serves as an effective tool for teaching derivative concepts, function graphing, and interactive mathematical exploration.