導(dǎo)數(shù)微分知識(shí)點(diǎn)

1、第二章導(dǎo)數(shù)與微分一、導(dǎo)數(shù)定義名稱定義記號(hào)函數(shù)在)x(f點(diǎn)可ox導(dǎo)設(shè)函數(shù)在點(diǎn)有定義)x(f)x(Uo，x)x(f)xx(flimxylim000x0x???????????存在，則在)ba()xx(0???)x(f0x點(diǎn)可導(dǎo)（或存在）00xxxx)x(f)x(flim0?????)x(f0x)x(f)xx(flim000x??????函數(shù)在)x(f上)ba(可導(dǎo)若函數(shù)在上每一點(diǎn)都可)x(f)ba(導(dǎo)，則稱函數(shù)在上可導(dǎo))x(f)ba(函數(shù)在

2、)x(f點(diǎn)左ox導(dǎo)數(shù)若極限存x)x(f)xx(flim000x???????在，則其為在點(diǎn)的左導(dǎo)數(shù))x(f0x（或存在）00xxxx)x(f)x(flim0???????)x(f0x)x(f)xx(flim000x???????函數(shù)在)x(f點(diǎn)右ox導(dǎo)數(shù)若極限存x)x(f)xx(flim000x???????在，則其為在點(diǎn)的右導(dǎo)數(shù))x(f0x（或存在）00xxxx)x(f)x(flim0???????)x(f0x)x(f)xx(flim

3、000x???????函數(shù)在)x(f上]ba[可導(dǎo)若函數(shù)在上每一點(diǎn)都可)x(f]ba[導(dǎo)，區(qū)間端點(diǎn)的導(dǎo)數(shù)理解為單側(cè)導(dǎo)數(shù)。)t())t()t((xydxydttx22???????????四、基本初等函數(shù)的求導(dǎo)公式（為常數(shù)）0)C(??Cxcos)x(sin??xtanxsec)x(sec??1x)x(??????xsin)x(cos???xcotxcsc)x(csc???)1a0a(alna)a(xx????xsec)x(tan2??2

4、x11)x(arctan???xxe)e(??xcsc)x(cot2???2x11)xcotarc(????)1a0a(alnx1)x(loga????)1x1(x11)x(arcsin2??????x1)x(ln??)1x1(x11)x(arccos2???????五、高階導(dǎo)數(shù)的基本公式x)n(xe)e(?nnx1n1)x(??????????）（）（）（?)2naxsin(a)ax(sinn)n(???)2nbxcos(b)bxco