Visualizing Derivatives of Exponential Functions

① This GeoGebra example dynamically demonstrates the derivative of an exponential function by showing the tangent line at a movable point and its slope value. ② It illustrates the core calculus concept that the derivative of e^x is e^x itself, and for a general base a, the derivative is a^x·ln(a), connecting the geometric tangent slope to the algebraic derivative formula. ③ Construction uses the commands Intersect to find the point A where the function f meets a vertical line, Tangent to create the tangent line g at A, and Slope to compute its slope; sliders a and b adjust the base and the x-coordinate of the point, with auxiliary objects B and C for labeling. ④ Suitable for high school or early college students learning differential calculus, as an interactive visual aid for understanding the derivative as a slope and the specific rules for exponential functions.