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# 英文的微積分問題

可以幫我翻譯一下並解答嗎：

a. Describe how to find the second derivative of a differentiable function.

b.What does the second derivative of a function represent relative to the first first derivative?Explain

B題我比較不懂他再問什麼 ，英數高手幫我解釋一下，感謝！

### 3 Answers

- FeIhOnG of OzLv 71 decade agoFavorite Answer
回版主, 翻譯和解答如下:a. Describe how to find the second derivative of a differentiable function.請敘述該如何算出可微函數的二階導數解答: 先將可微函數微分, 得出一階導數, 然後再將之微分一次即可得出二階導數.b.What does the second derivative of a function represent relative to the first first derivative?Explain相對於若干函數之一階導數來說, 其二階導數代表了什麼呢? 請解釋.解答: 由於二階函數是一階函數的微分, 所以對於一階函數來說, 二階函數就是其瞬間變化率的公式. 微分定義的中文解釋樓上一位大大已經解釋過了, 下面是摘自英文版的維基百科的解釋:In physical terms, differentiation expresses the rate at which a quantity, y, changes with respect to the change in another quantity, x, on which it has a functional relationship. Using the symbol Δ to refer to change in a quantity, this rate is defined as a limit of difference quotients

圖片參考：http://upload.wikimedia.org/math/2/a/4/2a433e72a7f...

as Δx approaches 0. In Leibniz's notation for derivatives, the derivative of y with respect to x is written

圖片參考：http://upload.wikimedia.org/math/e/f/a/efaf9f3a22d...

參考看看吧^^

2006-04-09 08:19:44 補充：

發現公式沒聯結上來, 請按維基百科的聯結即可看到.

Source(s): The Boy from Oz (澳洲男孩)- Login to reply the answers

- 1 decade ago
a. Describe how to find the second derivative of a differentiable function.

請描述如何尋找可微分函數中的二階導函數

b.What does the second derivative of a function represent relative to the first first derivative?Explain

一個函數中的二階導函數與一階導函數的關聯為何? 請解釋

the first derivative 一階導函數

the second derivative 二階導函數

derivative 導函數

a differentiable function 可微分函數

Source(s): ＯＢ＋網路- Login to reply the answers

- 1 decade ago
a.請敘述如何找到一個可微函數的二微導數

b.這個函數的二微導數代表著跟一微導數之間有什麼關聯呢？請解釋。

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給你一點概念

所謂

一次微分就是找出某一單位量的變化之下，

另一個對應的單位變化如何。

二次微分就是看這些對應的單位變化的趨勢，

例 ｆ＂＞０遞增,ｆ＂＝０相同,ｆ＂＜０遞減。

這可以用在很多很多科學計算，

非常實務！

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