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- Thread starter feynman1
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- #2

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These kinds of details help us decide on the level of response.

- #3

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Physics problem. It's one of taking the variation of an energy of an object with energy density F in the OP varying in space. f(x) can be a displacement, x can be a coordinate. df(x)/dt can be a speed. Clear?

These kinds of details help us decide on the level of response.

- #4

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From your notation, ##f## appears to be a function of only one variable; namely, x. In that case ##\frac{d(f(x))}{dt} = 0##.

For ##f## to have nonzero (partial) derivatives wrt x and t, it should use this notation: ##f(x, t)##. Then ##\frac{\partial f}{\partial x} = f_x((x, t)## and ##\frac{\partial f}{\partial t} = f_t((x, t)## would make sense.

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- #5

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right because I couldn't put a dot on top of f(x).From your notation, ##f## appears to be a function of only one variable; namely, x. In that case ##\frac{d(f(x))}{dt} = 0##.

For ##f## to have nonzero (partial) derivatives wrt x and t, it should use this notation: ##f(x, t)##. Then ##\frac{\partial f}{\partial x} = f_x((x, t)## and ##\frac{\partial f}{\partial t} = f_t((x, t)## would make sense.

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Well, not if ##x## itself depends on ##t##.##f## appears to be a function of only one variable; namely, x. In that case ##\frac{d(f(x))}{dt} = 0##.

To @feynman1: could you point us to a suitable reference? I'm not yet sure what you are asking.

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Sorry there's no direct reference as it's a work in progress. Physics problem. It's one of taking the variation of an energy of an object with energy density F in the OP varying in space. f(x,t) can be a displacement, x is a fixed coordinate not dependent on t. df(x,t)/dt can be a speed. Clear?Well, not if ##x## itself depends on ##t##.

To @feynman1: could you point us to a suitable reference? I'm not yet sure what you are asking.

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Not clear at all, sorry. I can't help until there's a clear problem statement.

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if that helpsNot clear at all, sorry. I can't help until there's a clear problem statement.

https://math.mit.edu/classes/18.086/2006/am72.pdf

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- #11

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Which would show up in a clearly posed question. If someone writes "f(x)" without anything further, the reasonable assumption is that f depends only on x, with no relationship to t.Well, not if x itself depends on t.

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sorry unable to edit the OP any moreWhich would show up in a clearly posed question. If someone writes "f(x)" without anything further, the reasonable assumption is that f depends only on x, with no relationship to t.

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only difference from trivial cases: the integrand has time dependent terms but the integral isn't over time, which isn't covered by variational calculus. Clear?

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No, not clear. You said "Physics Problem" more than once, but with no further detail, as if we're supposed to know clairvoyantly[...] because I couldn't put a dot on top of f(x). [...] only difference from trivial cases: the integrand has time dependent terms but the integral isn't over time, which isn't covered by variational calculus. Clear?

[

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- #15

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This...[Aside:You need to spell out your specific situation/problem explicitly. If you won't put more effort into composing your questions, why should other people put more effort into helping you? ]

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