Question: The outer product of two vectors is a second-order tensor with nine components. In Cartesian coordinates, it is The product rule applied to the divergence

The outer product of two vectors is a second-order tensor with nine components. In Cartesian coordinates, it is

FG FG FG FG= F,G, F,G, F,G FG FG FG

The product rule applied to the divergence of the product of two vectors F(vector) and G(vector) is written as

Expand both sides of this equation in Cartesian coordinates and verify that it is correct.

FG FG FG FG= F,G, F,G, F,G FG FG FG

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