導數(shù)微分知識點

1、第二章導數(shù)與微分一、導數(shù)定義名稱定義記號函數(shù)在)x(f點可ox導設函數(shù)在點有定義)x(f)x(Uo，x)x(f)xx(flimxylim000x0x???????????存在，則在)ba()xx(0???)x(f0x點可導（或存在）00xxxx)x(f)x(flim0?????)x(f0x)x(f)xx(flim000x??????函數(shù)在)x(f上)ba(可導若函數(shù)在上每一點都可)x(f)ba(導，則稱函數(shù)在上可導)x(f)ba(函數(shù)在

2、)x(f點左ox導數(shù)若極限存x)x(f)xx(flim000x???????在，則其為在點的左導數(shù))x(f0x（或存在）00xxxx)x(f)x(flim0???????)x(f0x)x(f)xx(flim000x???????函數(shù)在)x(f點右ox導數(shù)若極限存x)x(f)xx(flim000x???????在，則其為在點的右導數(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[可導若函數(shù)在上每一點都可)x(f]ba[導，區(qū)間端點的導數(shù)理解為單側(cè)導數(shù)。)t())t()t((xydxydttx22???????????四、基本初等函數(shù)的求導公式（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、高階導數(shù)的基本公式x)n(xe)e(?nnx1n1)x(??????????）（）（）（?)2naxsin(a)ax(sinn)n(???)2nbxcos(b)bxco