I know that for any C(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}function, the mixed second-order partials are equal, and I see that this should extend inductively to a statement about the kth partials of a C^{k}function, but I am having trouble figuring out exactly how this works.

For example, take f:ℝ^{2 }→ ℝ .

f_{xxy}=f_{xyy}is not true, right?

Folland'sAdvanced Calculussays that in Taylor's theorem we can use the notation [itex]\partial[/itex]^{[itex]\alpha[/itex]}f to refer to "the generic partial derivative of order [itex]|\alpha|[/itex], since the order of differentiation doesnt matter". ([itex]\alpha[/itex] is a multi-index)

But this doesnt make sense to me, considering that there are multiple possibilities for the order>2 partials, even when restricting it to mixed partials. Is this an oversight in Folland's wording, or am I missing something?

Thanks in advance for your replies :)

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# Equality of mixed partial derivatives of order >2

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