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From: eurms@apionet.or.jp (M_SHIRAISHI)
Newsgroups: fj.sci.math
Subject: Re: =?ISO-2022-JP?Q?Quiz=5F06iv2004=1B$B!J2rEz!K=1B(B?=
Date: 11 May 2004 00:24:36 -0700
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Xref: ccsf.homeunix.org fj.sci.math:1034

訂正。m(_ _)m
>
N_SHIRAISHI wrote in message news:<800c7853.0405102205.17793e09@posting.google.com>...
>
> Δ(Δx)＝Δ(x_1−x)＝{x_1−(x＋Δx)}−{x_1−x}＝−Δx
>
> ∴ lim{Δx→0}〔[{Δx＋Δ(Δx)}−Δx]／Δx〕
> ＝ lim{Δx→0}〔[{Δx)−Δx}−Δx]／Δx〕
> ＝ lim{Δx→0}〔−Δx／Δx〕
> ＝−1
>
> ∴ (Δx)'＝−1

Δ(Δx)＝Δ(x_1−x)＝{x_1−(x＋Δx)}−{x_1−x}＝−Δx

従って、導関数の、limit を用いた定義によっても、　

(Δx)'＝lim{Δx→0}〔Δ(x＋Δx)−Δx]／Δx〕
＝lim{Δx→0}〔{(x＋Δx＋Δ(x＋Δx)}−{x＋Δx}−Δx]／Δx〕
＝lim{Δx→0}〔{x＋Δx＋Δx＋Δ(Δx)}−{x＋Δx}−Δx]／Δx〕
＝lim{Δx→0}〔{x＋2Δx−Δx}−{x＋Δx}−Δx]／Δx〕
＝ lim{Δx→0}〔−Δx／Δx〕
＝−1

∴ (Δx)'＝−1