One often encounters the following identitiy in Tensor Analysis/Differential Geometry:(adsbygoogle = window.adsbygoogle || []).push({});

dx^j (partial/partial x^i) = partial x^j / partial x^i = delta ij

It's easy to see why partial x^j / partial x^i = delta ij

but how does

dx^j (partial/partial x^i) = partial x^j/partial x^i ?

I have three problems with this:

1. the dx^j involves an ordinary "d' and not a partial

2. somehow the dx^j gets moved in front of the partials

3. because when it moves we have (partial)(dx^j)/partial x^i, there are two derivatives on the top

Any explanation would be helpful. Thanks.

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# Proving an Identity from Differential Geometry

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