Derivatives of Inverse Exponential Functions

This example demonstrates the geometric meaning of derivatives of inverse exponential functions, dynamically showing the relationship between tangent lines and function graphs. Core math concepts include derivatives, exponential functions, inverse functions, tangent slope, and vector representation. Construction highlights involve commands like Mirror, Textfield, Point, Tangent, Slope, Circle, Intersect, and Vector to build function images, tangents, vectors, and intersection points. Suitable for high school mathematics teaching to understand the derivative rule of inverse functions and the dynamic change of tangents.