Derivative of Log Functions
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This example demonstrates the derivative of logarithmic functions. It involves key mathematical concepts such as logarithmic functions and their derivatives. By adjusting parameters, one can observe changes in the logarithmic function's graph and its derivative's properties. The construction summary mentions objects such as function f, parameter a, point A, constant c, integer n, function g, point B, and constant d. Suitable for high school mathematics education and learning about derivatives.
GeoGebra Commands & Parameters
f(x) = log(x)Numeric a(2)(a, log(a))y - f(a) = (1 / a * (x - a))Numeric n(0.1)g(x) = log((n * x))(a, g(a))y - g(a) = (1 / a * (x - a))
AI Drawing Prompt Reference
Draw the graph of a logarithmic function and its derivative. First, draw the function f(x)=ln(x). Then set parameter a=2 and draw the tangent line at point (a, ln(a)). Next, set step n=0.1 and draw the new function g(x)=ln(nx), and draw the tangent line at point (a, ln(n*a)).
The prompt above was compiled from the original drawing commands and is for reference only.