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I am trying to work through Spivak'sCalculus on Manifoldsover the holidays, and I am a little stuck on his proof of the unique derivative (on p. 16 as well as below).

Specifically,

(i) Why does the ≤ inequality hold, and

(ii) Why does the last equality of the second-to-last-line hold?

I would very much appreciate any help!

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# Proof of unique derivative

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