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Directional Derivatives

Keywords: Multivariable Calculus, Rate of Change, Directional Derivatives, Gradient, Master Formula, Surfaces

mvdderiv.jpg

Highlights of the activity

  1. This small group activity using surfaces relates the geometric definition of directional derivatives to the components of the gradient vector.
  2. Students work in small groups to measure a directional derivative directly, then compare its components with measured partial derivatives in rectangular coordinates.
  3. The whole class wrap-up discussion emphasizes the relationship between the geometric gradient vector and directional derivatives.

Reasons to spend class time on the activity

Clarifies the geometry of the gradient vector and its components.

Reflections

Instructor's Guide

Student Handouts

mvdderivhand.pdf


Authors: (c) Aaron Wangberg and the "Raising Calculus to the Surface" team; used by permission.
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