Introduction to Partial Derivatives

Introduction to Partial Derivatives
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2019-01-03 09:49
This example demonstrates the geometric meaning of partial derivatives by visualizing the direction of the derivative at a point on a function. Key math concepts include derivatives, vectors, function graphs, and linear equations. Construction highlights the use of GeoGebra commands like Vector and Line, along with objects such as f (function), f_x (x-direction partial derivative), and f_y (y-direction partial derivative). Suitable for university-level calculus beginners or teaching purposes.

GeoGebra Commands & Parameters

  1. Vector(A, A + (-0.5 / a, 0, -0.5)) → u
  2. Vector(A, A + (0, 0.5 / b, 0.5)) → v
  3. Vector(A, A + ((-a), (-b), 1)) → w
  4. Line((x(A), y(A), z(A)), Vector[(x(u), y(u), z(u))]) → r
  5. Line((x(A), y(A), z(A)), Vector[(x(v), y(v), z(v))]) → s