一、導(dǎo)數(shù)的運(yùn)算法則
1.和差的導(dǎo)數(shù)
[f(x)±g(x)]′=f′(x)±g′(x).
2.積的導(dǎo)數(shù)
(1)[f(x)g(x)]′=f′(x)g(x)+f(x)g′(x);
(2)[cf(x)]′=cf′(x).
3.商的導(dǎo)數(shù)
=,g(x)≠0.
二、復(fù)合函數(shù)的概念及求導(dǎo)法則
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復(fù)合函數(shù)的概念
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一般地,對(duì)于兩個(gè)函數(shù)y=f(u)和u=g(x),如果通過(guò)變量u,y可以表示成x的函數(shù),那么稱這個(gè)函數(shù)為函數(shù)y=f(u)和u=g(x)的復(fù)合函數(shù),記作y=f(g(x)).
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復(fù)合函
數(shù)的求
導(dǎo)法則
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復(fù)合函數(shù)y=f(g(x))的導(dǎo)數(shù)和函數(shù)y=f(u),u=g(x)的導(dǎo)數(shù)間的關(guān)系為=·,即y對(duì)x的導(dǎo)數(shù)等于y對(duì)u的導(dǎo)數(shù)與u對(duì)x的導(dǎo)數(shù)的乘積.
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1.判斷(正確的打“√”,錯(cuò)誤的打“×”)
(1)若f′(x)=2x,則f(x)=x2. ( )
(2)已知函數(shù)y=2sin x-cos x,則y′=2cos x+sin x. ( )
(3)已知函數(shù)f(x)=(x+1)(x+2),則f′(x)=2x+1. ( )
[解析] (1)由f′(x)=2x,則f(x)=x2+c.
(2)由y=2sin x-cos x,