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For real valued functions of a real variable, is there a global criterion for differentiability?

I feel there should be, as there is a global criterion for continuity - that the inverse of every open set is open. This criterion is global in the sense that it does not refer to any particular point.

fdzsfhaS
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    I'm not sure that I see how "the inverse image of every open set is open" is a global property. Indeed, this seems like the very definition of a local property (i.e. every point in the codomain is contained in a neighborhood with open preimage). This question on MSE is relevant. – Xander Henderson Jan 05 '20 at 21:55
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    I'm looking for a criterion that does not refer to any particular point. If you don't want to call that global, that is fine – fdzsfhaS Jan 05 '20 at 22:00

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