Graphing the First Derivative from the Graph of a Function

① This example demonstrates how to construct the graph of the first derivative of a given function f by dynamically placing tangent lines and tracking their slopes. ② The core mathematical concept is the geometric interpretation of the derivative: the derivative at a point equals the slope of the tangent line at that point, and the derivative graph reflects the rate of change of the original function. ③ Construction details: using GeoGebra commands such as Point to place a movable point A on the function graph, Tangent to create the tangent line g at A, Slope to compute the slope value, and Segment to visualize the slope as a segment. Buttons and a counter (button1, button2, button3, button4, counter) are used to step through points, gradually building the derivative curve. ④ Suitable for high school calculus introduction or pre-university levels, this interactive tool helps students visualize the derivative concept and graph transformations, and can be used for classroom demonstrations or self-paced exploration.