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which is the derivative of U with respect to x,
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and is going to have a y component
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which is the derivative of U with respect to y.
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That is step two.
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In fact, the claim now is
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this force is going to be a conservative force.
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And in fact, this potential energy
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associated with it will be the function you started with.
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So, how do I know that?
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So, for example, I'm saying suppose U = x·y^3,
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then Fx = - dU / dx,
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which is equal to - y^3,