From 4c0f40862bee977127fe2e3f943a3d637dbb5372 Mon Sep 17 00:00:00 2001 From: unlockable Date: Thu, 3 Nov 2022 15:27:07 +0800 Subject: [PATCH] =?UTF-8?q?=E4=BF=AE=E6=94=B9=E5=87=A0=E4=B8=AA=E5=B0=8F?= =?UTF-8?q?=E9=94=99=E3=80=82?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 03函数的导数.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/03函数的导数.tex b/03函数的导数.tex index db188ff..1f64fe7 100644 --- a/03函数的导数.tex +++ b/03函数的导数.tex @@ -135,19 +135,19 @@ Leibniz记号：记$\Delta f = f(x_0 + \delx) - f(x_0)$，那么 \end{theorem} \begin{remark} - 用Leibniz记号上式可化为 + 用Leibniz记号上式可记为 \[\frac{\dif y}{\dif t} = \frac{\dif y}{\dif x} \cdot \frac{\dif x}{\dif t}\] \end{remark} \begin{proof} - $\deriv{f}(x) = \tolim{\delx}{0}\frac{\Delta y}{\Delta x}$。 + $\deriv{f}(x) = \tolim{\delx}{0}\dfrac{\Delta y}{\Delta x}$。 思路： \begin{align*} - \tolim{\Delta t}{0} \frac{\Delta y}{\Delta x} & = \tolim{\Delta t}{0} \frac{\Delta y}{\Delta x} \cdot \frac{\Delta x}{\Delta t}\\ + \tolim{\Delta t}{0} \frac{\Delta y}{\Delta t} & = \tolim{\Delta t}{0} \frac{\Delta y}{\Delta x} \cdot \frac{\Delta x}{\Delta t}\\ \intertext{注意：这里不能保证$\Delta x \neq 0$} & = \tolim{\Delta t}{0} \frac{\Delta x}{\Delta t} \cdot \tolim{\Delta x}{0} \frac{\Delta y}{\Delta x}\\ & = \deriv{\varphi}(t) \cdot \deriv{f}(x)\\ - & = \deriv{\varphi}(t) \cdot \deriv{f}(\varphi((t))) + & = \deriv{\varphi}(t) \cdot \deriv{f}(\varphi(t)) \end{align*} 因此证法为：$\Delta x \neq 0$时，引入记号