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Classroom Tips and Techniques: Directional Derivatives in Maple

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Several identities in vector calculus involve the operator A . (VectorCalculus[Nabla]) acting on a vector B. The resulting expression (A . (VectorCalculus[Nabla]))B is interpreted as the directional derivative of the vector B in the direction of the vector A. This is not easy to implement in Maple's VectorCalculus packages. However, this functionality exists in the Physics:-Vectors package, and in the DifferentialGeometry package where it is properly called the DirectionalCovariantDerivative. This article examines how to obtain (A . (VectorCalculus[Nabla]))B in Maple.