[微積] Chain rule 的證明
想請教一下關於證明過程的一點問題
前半段我看得懂，但是後半段不是很了解
為什麼當Δx=0時令ε趨近於0，會使得ε是一個Δx的連續函數?
f'(a)是一個常數，那Δy應該當成變數還是常數或是其他東西?
然後為什麼下一行的定義(?)又變成Δx→0?
有請貴人相助
謝謝
原文
If we denote by ε the difference between the difference quotient and
derivature, we obtain
Δy
lim ε = lim (--- — f'(a) ) = f'(a) - f'(a) = 0
Δx→0 Δx→0 Δx
But
Δy
ε = --- — f'(a) ) => Δy=f'(a)Δx + εΔx
Δx
If we define ε to be 0 when Δx=0, then εbecomes a continuous
function of Δx. Thus, for a differentiable function f, we can write
Δy = f'(a)Δx + εΔx = [f'(a) + ε]Δx where ε→0 as Δx→0
and ε is a continuous function of Δx.
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