Derivative of Logarithmic Function: Change Base a to Explore Slope

①This example dynamically demonstrates how the graph of a logarithmic function and its derivative change as the base a is adjusted via a slider or text input, with the tangent slope at a point displayed in real time.②The core mathematical concept is the derivative rule for logarithmic functions: if f(x)=log_a(x), then f'(x)=1/(x·ln a), where the base a directly affects the shape and magnitude of the derivative curve.③Construction highlights: using GeoGebra's Textfield to input the base a, creating the function f and its derivative f', and linking inputBox1, Text1, and Text2 to provide interactive control and dynamic text output, allowing users to change the base and instantly observe the resulting graphs and slope values.④This is suitable for high school to undergraduate calculus instruction, particularly for teaching logarithmic differentiation, the influence of the base on the derivative, and the relationship between a function and its derivative graph. It also serves well for self-study and classroom demonstrations.