- 五年制高職數(shù)學(xué)(第三冊)
- 張瑾 鄒秀英 趙春芳
- 599字
- 2020-06-29 11:36:42
思考與總結(jié)
一、導(dǎo)數(shù)與微分的概念與結(jié)論
1.導(dǎo)數(shù)的概念
(1)導(dǎo)數(shù)的定義:__________.
(2)導(dǎo)數(shù)f′(x0)的幾何意義:__________,切點(diǎn)處的切線方程:__________;法線方程:__________.
(3)導(dǎo)數(shù)f′(t0)的物理意義:__________;二階導(dǎo)數(shù)f″(t0)的物理意義:__________.
(4)函數(shù)在x0點(diǎn)連續(xù)與可導(dǎo)的關(guān)系:__________.
(5)高階導(dǎo)數(shù)的記號與求法:__________.
2.微分的概念
(1)f(x)在任意點(diǎn)x處的微分:__________.
(2)微分與導(dǎo)數(shù)的關(guān)系:__________.
二、導(dǎo)數(shù)與微分的基本公式與運(yùn)算法則
1.基本初等函數(shù)的導(dǎo)數(shù)公式
(1)(c)′=__________(c為常數(shù)); (2)(xα)′=__________(α為任意實(shí)數(shù));
(3)(x)′=__________; (4)(x2)′=__________;

(7)(ax)′=__________(a>0,a≠1);(8)(ex)′=__________;
(9)(logax)′=__________; (10)(ln x)′=__________;
(11)(sin x)′=__________; (12)(cos x)′=__________;
(13)(tan x)′=__________; (14)(cotx)′=__________;
(15)(secx)′=__________; (16)(cscx)′=__________;
(17)(arcsin x)′=__________; (18)(arccos x)′=__________;
(19)(arctan x)′=__________; (20)(arccotx)′=__________.
2.導(dǎo)數(shù)的四則運(yùn)算法則
(1)(u±v)′=__________; (2)(uv)′=__________;
(3)(cu)′=__________; (4)=__________(v≠0);
(5)=__________(v≠0,c為常數(shù))
3.復(fù)合函數(shù)的求導(dǎo)法則:__________.
(1)若u=u(x)可導(dǎo),則(sin u)′x=__________;(ln u)′x=__________.
(2)若u=2x,則(cos 2x)′=__________;(arctan 2x)′=__________.
4.隱函數(shù)的求導(dǎo)法:__________.
5.微分形式的不變性:__________.
(1)d(eu)=__________;(2)(uα)′=__________(α∈R);(3)(tan u)′=__________.
三、可導(dǎo)、可微、連續(xù)與極限存在的關(guān)系:
可微__________可導(dǎo)__________連續(xù)__________極限存在.
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