Exploring the Derivative of Exponential Functions by Mak Desmond (2)

This interactive GeoGebra example dynamically illustrates how the slope of the tangent line to an exponential function changes as a point moves along the curve, revealing the key property that the derivative of an exponential function is proportional to the function itself. Core mathematical concepts include exponential functions, derivatives, tangent lines, and rates of growth. The construction uses GeoGebra commands such as Point to create a movable point A on the graph, Tangent to draw the tangent line at that point, Slope to compute and display the slope value, and Name/LaTeX for labeling the function, points, and slope expressions. Additional objects like auxiliary points (A1, B1, etc.) and text boxes are included to compare slopes at different locations or for different bases, likely controlled by sliders a and b. This resource is suitable for high school or introductory college calculus students to grasp the geometric meaning of derivatives of exponential functions, especially the special role of the base e, and can be used for classroom demonstrations or self-directed exploration.