1.導(dǎo)數(shù)的概念
稱函數(shù)y=f(x)在x=x0處的瞬時變化率li=li為函數(shù)y=f(x)在x=x0處的導(dǎo)數(shù),記作f′(x0)或y′|x=x0,即f′(x0)=li=li.稱函數(shù)f′(x)=li為f(x)的導(dǎo)函數(shù).
2.基本初等函數(shù)的導(dǎo)數(shù)公式
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基本初等函數(shù)
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導(dǎo)函數(shù)
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f(x)=c (c為常數(shù))
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f′(x)=
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f(x)=sin x
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f′(x)=cos_x
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f(x)=ex
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f′(x)=
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f(x)=ln x
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f′(x)=
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基本初等函數(shù)
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導(dǎo)函數(shù)
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f(x)=xα(α∈Q*)
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f′(x)=αxα-1
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f(x)=cos x
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f′(x)=-sin_x
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f(x)=ax(a>0,a≠1)
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f′(x)=axln_a
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f(x)=logax(a>0,a≠1)
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f′(x)=
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3.導(dǎo)數(shù)運算法則
(1)[f(x)±g(x)]′=f′(x)±g′(x);
(2)[f(x)·g(x)]′=f′(x)g(x)+f(x)g′(x);
(3)′=(g(x)≠0).
4.復(fù)合函數(shù)的導(dǎo)數(shù)
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yx′=yu′·ux′,即y對x的導(dǎo)數(shù)等于y對u的導(dǎo)數(shù)與u對x的導(dǎo)數(shù)的乘積.