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Derivative of Natural Log: y=ln(x)

Derivative of Natural Log: y=ln(x)
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2014-06-18 17:22
FunctionCalculusDerivativeGeometric ConstructionGraphing
This example demonstrates the calculation and geometric meaning of the derivative of the natural logarithm function y=ln(x). Key math concepts include the definition of derivatives, tangent slope, and function graph transformations. GeoGebra commands/objects used in construction summary are Point, Segment, Line, Mirror. Suitable for high school mathematics teaching to understand the derivative formula of logarithmic functions and its visualization process.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Segment(A, B) → a
  3. Segment(B, C) → b
  4. Line(A, C) → c
  5. Mirror(A, d) → A'
  6. Mirror(B, d) → B'
  7. Mirror(C, d) → C'
  8. Line(A', C') → e
  9. Segment(A', B') → h
  10. Segment(C', B') → i

AI Drawing Prompt Reference

Draw the graph of the natural logarithm function y=ln(x) and show its derivative geometrically. First, plot the function curve, then take a point on the curve and draw the tangent line at that point, indicating the slope of the tangent. Next, perform a symmetry operation to obtain the symmetric relationship between the tangent line and the function curve, and finally display the symmetric graph and tangent line to help understand the concept and geometric meaning of the derivative.
The prompt above was compiled from the original drawing commands and is for reference only.