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superfahd

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in the 1st half hour, he gives a proof of the law of conservation of energy. In the course of this proof he uses the formula: F = - [tex]\vec{}\nabla[/tex] U (x, y). Where U(x,y) is the potential energy of a particle at position (x,y). I don't remember any such formula from my secondary school classes. Can someone please explain to me how this formula comes out and what it even means?

Also he then writes: d U(x,y) / dt = [tex]\Sigma[/tex]

_{i}[tex]\partial[/tex]U/[tex]\partial[/tex]X

_{i}.[tex]\dot{}X[/tex] +[tex]\partial[/tex]U/[tex]\partial[/tex]Y

_{i}.[tex]\dot{}Y[/tex] (I'm not sure if I rendered the formula correctly. This latex thing is confusing). How does he arrive to this? I realize that differentiation concepts need a lot of review but I'm only doing this as a hobby so can someone explain it to me as such? Thanks a lot