# 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.

Â© BrainMass Inc. brainmass.com March 4, 2021, 7:38 pm ad1c9bdddfhttps://brainmass.com/math/derivatives/vectors-product-rule-gradient-curl-113881

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= 2x + y + 4z

= 2y - 3x

For the following ...

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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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