- #1
John777
- 27
- 1
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*(UxVx + UyVy + UzVz)
The right side is [tex]\delta[/tex]/[tex]\delta[/tex]x*(VxUx + VyUy + VzUz +
VyUz)
does the VyUz 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 UxVx
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.
The right side is [tex]\delta[/tex]/[tex]\delta[/tex]x*(VxUx + VyUy + VzUz +
VyUz)
does the VyUz 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 UxVx
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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