Exponential Functions and Euler's Number e: Derivative Exploration

This GeoGebra example demonstrates how exponential functions and their derivatives change as the base varies, with special emphasis on Euler's number e, where the exponential function is equal to its own derivative. Core mathematical concepts covered include exponential functions, derivatives, Euler's number, function graphing, transformations, symmetry, and arithmetic operations. The construction relies on GeoGebra commands If and Derivative, utilizing objects a_1, g, a, b, f, h, c, p to define functions, compute derivatives, and control conditional display and dynamic behavior. It is suitable for high school calculus introductions and university-level mathematical analysis, serving as a classroom demonstration tool or an interactive resource for independent exploration of exponential derivative properties.