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The Gradient Vector and Directional Derivative

The Gradient Vector and Directional Derivative
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2015-09-11 05:21
VectorCalculusGeometric Construction

GeoGebra Commands & Parameters

  1. Circle(D, 1) → g
  2. Point(g) → G
  3. Point(xAxis) → C
  4. Point(yAxis) → B
  5. Segment((24, 0), (24, P)) → a
  6. Vector(D, D + (((((-1 * 8) * exp((-1 * x(D)^(2)) - y(D)^(2))) * x(D)) * y(D)), (4 * exp((-1 * x(D)^(2)) - y(D)^(2))) - ((8 * exp((-1 * x(D)^(2)) - y(D)^(2))) * y(D)^(2)))) → gradient
  7. Vector(D, G) → u
  8. Length(gradient) → b
  9. Length(gradient) → normGrad
  10. Vector(D, D + (u * du)) → proj

AI Drawing Prompt Reference

Draw a graph showing the gradient vector of a function. Start by drawing a unit circle g, then take a point C on the x-axis and a point B on the y-axis. Choose a point D on the circle, draw a perpendicular segment a from D to the x-axis. Calculate the gradient vector at D, then draw a vector u from D to G. Compute the length b and norm normGrad of the gradient vector. Finally, draw the projection proj of the gradient vector in the direction of u.
The prompt above was compiled from the original drawing commands and is for reference only.