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I am trying to prove two things equal that involves a bunch of dot products, cross products and curls. I can't remember the exact problem, but this demonstrates my question.

My question is the left side [tex]\delta[/tex]/[tex]\delta[/tex]x*(U

The right side is [tex]\delta[/tex]/[tex]\delta[/tex]x*(V

V

does the V

Also do the the other terms become 1 since for example in the partial deriv wrt x of U

If my explanation did not make sense here is the original problem grad(U.V) = (U.grad)V + (Vxgrad)U + Ux(gradxV) + Vx(gradxU)

Just looking at the i component The left side yields partial deriv wrt x of (UxVx + UyVy + UzVz)i

The right side however yields terms in the i component that are partials wrt to x, y and z.

My question is the left side [tex]\delta[/tex]/[tex]\delta[/tex]x*(U

_{x}V_{x}+ U_{y}V_{y}+ U_{z}V_{z})The right side is [tex]\delta[/tex]/[tex]\delta[/tex]x*(V

_{x}U_{x}+ V_{y}U_{y}+ V_{z}U_{z}+V

_{y}U_{z})does the V

_{y}U_{z}term cancel since the partial deriv wrt x is 0?Also do the the other terms become 1 since for example in the partial deriv wrt x of U

_{x}V_{x}If my explanation did not make sense here is the original problem grad(U.V) = (U.grad)V + (Vxgrad)U + Ux(gradxV) + Vx(gradxU)

Just looking at the i component The left side yields partial deriv wrt x of (UxVx + UyVy + UzVz)i

The right side however yields terms in the i component that are partials wrt to x, y and z.

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