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Derivative of arccot

Derivative of arccot
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2015-06-23 23:09
FunctionTrigonometryCoordinate GeometryCalculusDerivative
This example demonstrates the derivative of the arccotangent function. Key mathematical concepts include inverse trigonometric functions and derivatives. Using GeoGebra commands such as CurveCartesian, Function, Tangent, and Slope, the arccotangent function and its derivative are constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. CurveCartesian(1 / tan(t), t, t, 0, 3.141592653589793) → fO
  2. Point(fO) → F
  3. Vector(XOl, XOr) → u
  4. Vector(YOd, YOu) → v
  5. Vector(XDl, XDr) → w
  6. Vector(YDd, YDu) → z
  7. Function(-1 / (1 + x^(2)), x(XOl), x(XOr)) → gO
  8. Function(gO(x) + td, x(XOl), x(XOr)) → g
  9. Segment(AD, E) → e
  10. Tangent(F, fO) → a
  11. Slope(a) → m
  12. Segment(F, A) → c

AI Drawing Prompt Reference

Draw the arccotangent function and its derivative. First, plot the arccotangent function y=arccot(x). Then, choose a point F on the x-axis and draw the tangent line at point F. Calculate the slope m of the tangent line. Finally, draw a line segment from the origin to point F.
The prompt above was compiled from the original drawing commands and is for reference only.