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Understanding the Chain Rule

Understanding the Chain Rule
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2018-12-17 11:35
FunctionCalculusDerivative
This example demonstrates how the derivative of a composite function $f(g(x))$ depends on the derivatives of both $f$ and $g$. By dynamically adjusting the functions $f$ and $g$, one can intuitively understand the essence of the chain rule. The construction involves points, functions, and slider animations in GeoGebra. Suitable for teaching derivatives in calculus courses.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Segment(A, P1) → l1
  3. Segment((0, g(a)), (a, g(a))) → l2a
  4. Segment((a, g(a)), (g(a), g(a))) → l2b
  5. Segment((g(a), g(a)), (g(a), f(g(a)))) → l3a
  6. Segment((g(a), f(g(a))), (g(a), 0)) → l3b
  7. Segment((g(a), f(g(a))), (0, f(g(a)))) → l4a
  8. Polygon({Corner[2], Corner[1], (4 / 5 * Corner[1]) + (1 / 5 * Corner[4]), (4 / 5 * Corner[2]) + (1 / 5 * Corner[3])}) → console
  9. Textfield(g) → InputBox1
  10. Textfield(f) → InputBox2