Yeah I can’t lie, there is no calling this a daily challenge now.
Anyhow, have a go at proving this, I don’t want any unrigorous “imagine zooming in until the line is straight” nonsense.
Difficulty: not a lot
Would appreciate if u put ur proofs or attempts below, I got a proof but it’s like kinda mediocre.
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Substitute u = ah, rewrite to a × (standard def of derivative with u -> 0)? Lim h -> 0 implies u-> 0 (easily prooven using epsilon delta), so I think that should suffice?
![[2024/11/06] Derivative with multiple of differential](https://lemmy.world/pictrs/image/b94d7558-45a8-4751-95c7-875eaea017fa.png){kind=link}