s32微分公式和法则 、导数公式和微分公式 、导数法则和微分法则
§3.2 微分公式和法则 一、导数公式和微分公式 二、导数法则和微分法则
微分的求法: y 即计算函数的导数乘以自变量的微分 求导数和求微分的方法统称为微分法
微分的求法: dy=ydx 即计算函数的导数,乘以自变量的微分 求导数和求微分的方法统称为微分法
导数公式和微分公式 (1)(C)′=0 d(C=0 (2)(xa '=axa-I d(xa=axra-Idx (3)(ogax)= ina ddoga x)=dx n r d (n x)= ((ar)'=alna d(a=a lnadx (er=at d(e=edx
一、导数公式和微分公式 (1) (C)=0 d(C)=0 (2) (x )=x −1 d(x )=x −1dx x a a x ln 1 (3)(log ) = x a dx d a x ln (log ) = x x 1 (ln ) = x dx d(ln x) = (4) (a x )=a x lna d(a x )=a x lnadx (e x )=a x d(e x )=e xdx
(5(sinx)=cosx d(sinx =cosxdx (cosxr'=-sinx d(cosx)=-sinxdx (tanx)'=sec2x d(tanx)=seclxdx (cotx)=-csclx d(cotx)= scrap (secx)'-secxtanx d(secx =secxtanxdx (cscx)=-cscxcotx d(cscr)=-cscxcotxdx
(5) (sinx)=cosx d(sinx)=cosxdx (cosx)= −sinx d(cosx)= −sinxdx (tanx)=sec2x d(tanx)=sec2xdx (cotx)= −csc2x d(cotx)= −csc2xdx (secx)=secxtanx d(secx)=secxtanxdx (cscx)= −cscxcotx d(cscx)= −cscxcotxdx
(6)(arcsin x) d(arcsin x) dx 1-x (arccos x) d (arccos x)=-dx (arctan x) 1+x 2 d(arctan x) 1+x (arc cot x) d (arc cot x) dx 1+x 1+x
2 1 1 (6)(arcsin ) x x − = 2 1 (arcsin ) x dx d x − = 2 1 1 (arccos ) x x − = − 2 1 (arccos ) x dx d x − = − 2 1 1 (arctan ) x x + = 2 1 (arctan ) x dx d x + = 2 1 1 (arc cot ) x x + = − 2 1 (arc cot ) x dx d x + = −
导数法则和微分法则 (1(u+yy'=u'ty' d(utv=dutdv (2)(uvy'=u'vtuv' d(uv)=vdutudv (Cv)=Cy d(cy=Cdv (3)( uy vau-udv p 2 dy=yu'uy dx
二、导数法则和微分法则 (1) (uv)=uv d(uv)=dudv (2) (uv)=uv+uv d(uv)=vdu+udv (Cv)=Cv d(Cv)=Cdv 2 (3)( ) v u v uv v u − = 2 ( ) v vdu udv v u d − = 2 ) 1 ( v v v = − 2 ) 1 ( v dv v d = − (4) yx =yu ux dy=yu ux dx