Derivative of Natural Log Function - Interactive Exploration
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BC Calculus
① This GeoGebra example dynamically demonstrates the derivative of the natural logarithm function f(x)=ln(x) by showing how the slope of the tangent line changes along the curve. ② Core mathematical concepts include the definition of the derivative, tangent line slope, the derivative formula d/dx ln(x)=1/x, and the relationship between a function and its derivative graph. ③ Construction details: Based on the summary, the construction uses GeoGebra commands such as Point, Circle, Tangent, Intersect, and Vector, along with objects like function f, point A, circle c, tangent line g, intersection points B and C, vectors u, v, h, buttons, and text, enabling interactive discovery. ④ Suitable for senior high school or introductory college calculus students, this resource serves as an inquiry-based learning tool for understanding the geometric meaning of derivatives, and can also be used by teachers for classroom demonstrations.
GeoGebra Commands & Parameters
Point(f) → ACircle(A, 1.5) → cTangent(A, f) → gIntersect(c, g, 2) → BIntersect(c, g, 1) → CVector(A, B) → uVector(A, C) → v
AI Drawing Prompt Reference
Draw the graph of a natural logarithm function and dynamically show its derivative. Start by plotting the function curve, then select a point on the curve and draw a circle centered at this point. Next, draw a tangent line from the point, find the intersection points of the tangent with the circle. Finally, draw vectors from the center point to these two intersection points to visually represent the slope change of the tangent, revealing the geometric meaning of the derivative.
The prompt above was compiled from the original drawing commands and is for reference only.