andreasdr
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 Oct24 awarded Popular Question Oct15 awarded Autobiographer Jul2 awarded Curious Apr28 accepted Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity Apr28 revised Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity added 1 character in body Apr13 awarded Critic Apr13 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! Apr13 accepted Why aren't these partial derivatives interchangeable? Apr13 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. Apr13 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. Apr13 revised Why aren't these partial derivatives interchangeable? deleted 1 characters in body Apr13 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 $0$? Apr13 comment Why aren't these partial derivatives interchangeable? Please see the edit! Apr13 comment Why aren't these partial derivatives interchangeable? I've added an edit, trying to clear it up! Apr13 revised Why aren't these partial derivatives interchangeable? added 1126 characters in body Apr13 asked Why aren't these partial derivatives interchangeable? Mar21 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. Mar21 answered Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity Mar20 revised Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity added 23 characters in body Mar20 asked Problem with Taylor (asymptotic) expansion of hyperbolic functions at infinity