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Can anyone guide me to what this theorem is called or to its implications? Also, does it work in reverse? i.e. if it is true that d/dx(df/dy) = d/dy(df/dx) for some function f, then does f necessarily exist?

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- Thread starter Physics_wiz
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- #1

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Can anyone guide me to what this theorem is called or to its implications? Also, does it work in reverse? i.e. if it is true that d/dx(df/dy) = d/dy(df/dx) for some function f, then does f necessarily exist?

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HallsofIvy

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I remember before reading bits and pieces about how if we have a function of two variables, say f = f(x,y), then it must be true that d/dx(df/dy) = d/dy(df/dx), where the "d"'s are partials.

If f doesCan anyone guide me to what this theorem is called or to its implications? Also, does it work in reverse? i.e. if it is true that d/dx(df/dy) = d/dy(df/dx) for some function f, then does f necessarily exist?

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