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Derivatives don't always act like fractions (2021)
As an undergrad I learned a lot about partial derivatives in physics classes. But they told us rules as needed, without proving them. This rule completely freaked me out. If derivatives are …
As an undergrad I learned a lot about partial derivatives in physics classes. This proof is more sophisticated than my simple argument, but it’s very pretty, and it generalizes to higher dimensions in ways that’d be hard to guess otherwise. Actually he forgot to write down this particular equation at the top of his short proof—but he wrote down three others of the same form, and they all work the same way.
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