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seen Jun 3 at 11:13

Jul
2
awarded  Curious
Apr
28
accepted Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity
Apr
28
revised Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity
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Apr
13
awarded  Critic
Apr
13
comment Why aren't these partial derivatives interchangeable?
Oh that's right, the $t$:s should actually be seen as separate variables, i.e. we have the variable sets $(g, T)$ and $(x, t)$, so $\frac{\partial f}{\partial t}$ isn't ambiguous. Thanks!
Apr
13
accepted Why aren't these partial derivatives interchangeable?
Apr
13
comment Why aren't these partial derivatives interchangeable?
Many concepts unfamiliar to me up there, but thanks! :) I will ponder it more, but I think the conclusion of this whole discussion is that the partial derivatives I'm using in some sense deviate from the traditional ones (which don't (need to) specify what is held constant) and don't necessarily commute.
Apr
13
comment Why aren't these partial derivatives interchangeable?
But doesn't the concept of the chain rule for nested, multivariable functions (which is what my example in the edit above is about) require specifying what is held constant? I see no way of reformulating my use of the chain rule above without it.
Apr
13
revised Why aren't these partial derivatives interchangeable?
deleted 1 characters in body
Apr
13
comment Why aren't these partial derivatives interchangeable?
$\partial_{t|x}(\cdot)$ means "differentiate $(\cdot)$ wrt. $t$, keeping $x$ constant". So $\partial_{t|x}(x)$ means "differentiate $x$ wrt. $t$ keeping $x$ constant. Well, then we're differentiating a constant wrt. $t$, which surely must result in $0$?
Apr
13
comment Why aren't these partial derivatives interchangeable?
Please see the edit!
Apr
13
comment Why aren't these partial derivatives interchangeable?
I've added an edit, trying to clear it up!
Apr
13
revised Why aren't these partial derivatives interchangeable?
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Apr
13
asked Why aren't these partial derivatives interchangeable?
Mar
21
comment Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity
That helps a lot, thanks! I've expanded the idea behind your comment in an answer below.
Mar
21
answered Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity
Mar
20
revised Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity
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Mar
20
asked Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity
Dec
20
awarded  Yearling
Nov
3
awarded  Nice Answer