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    Vectors : Product Rule, Gradient and Curl

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    Trying to "prove" the following product rule for vector derivatives given the functions:

    vec{A} = 2x x-hat + y y-hat + 4z z-hat

    and

    vec{B} = 2y x-hat - 3x y-hat

    for the following product rule:

    Del(A.B) [Gradient of A.B] = A X (curl B) + B X (curl A) + (A.Del)B + (B.Del)A

    where I denoted the gradient as Del.

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    https://brainmass.com/math/derivatives/vectors-product-rule-gradient-curl-113881

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    = 2x + y + 4z
    = 2y - 3x

    For the following ...

    Solution Summary

    Vectors, Product Rule, Gradient and Curl are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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