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Derivative of Tan Graph

Derivative of Tan Graph
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2013-04-23 12:28
FunctionTrigonometryCalculusDerivativeGraphing
In collections Additional Mathematics (Derivatives)
This example demonstrates the derivative (tangent slope) of the tangent function graph. It involves core math concepts like derivatives, tangent slopes, asymptotes, function graphs, and periodicity. Construction highlights the use of GeoGebra commands such as Point, Tangent, Slope, Derivative, and Sliders to dynamically show the derivative properties of the tangent function. Suitable for high school and above students learning calculus and function graph analysis.

GeoGebra Commands & Parameters

  1. Point(f) → P_4
  2. Point(f) → P_1
  3. Point(f) → P_5
  4. Point(f) → P_7
  5. Point(f) → P_2
  6. Point(f) → P_3
  7. Tangent(P, f) → tangent
  8. Slope(tangent) → m
  9. Derivative(f) → f'

AI Drawing Prompt Reference

Draw the graph of the tangent function and its derivative, which is the slope of the tangent line. Select five points on the tangent curve and draw tangent lines at each point, calculating the slope of each tangent line. Represent the tangent function with a red curve and its derivative with a blue curve. The derivative curve should show the slope changes of the tangent function, including infinite slopes near the asymptotes. Adjust a slider dynamically to observe the periodicity and symmetry of both the tangent function and its derivative.
The prompt above was compiled from the original drawing commands and is for reference only.