Derivative of e(x): Tangent Line Visualization

This GeoGebra example dynamically illustrates the derivative of the exponential function e(x) by constructing the tangent line at a movable point A on the curve. It demonstrates the geometric meaning of the derivative as the slope of the tangent, and highlights the unique property that the derivative of e^x is itself. The construction uses the Tangent command with objects f (the function), a (a parameter or x-coordinate), A (the point), and g (the resulting tangent line). Vectors and coordinates are likely used to display the slope vector and point coordinates, making the relationship between the function and its derivative visually explicit. This resource is suitable for high school or introductory college calculus students, serving as an interactive tool for exploring the derivative concept, the exponential function's self-derivative property, and the connection between algebraic derivatives and graphical tangents. It can be used for self-study, classroom demonstrations, or as a basis for further exploration of derivative rules.