§ 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,
dy=y?dx
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 微分法一、导数公式和微分公式
(1) (C)?=0 d(C)=0
(2) (x?)?=?x1 d(x?)=?x1dx
axxa ln
1)( l o g )3(
ax
dxxd
a ln)( l o g?
xx
1)( l n
x
dxxd?)( l n
(4) (ax)?=axlna d(ax)=axlnadx
(ex)?=ax d(ex)=exdx
(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
21
1)( a r c s in )6(
x
x

21
)( a r c s i n
x
dxxd
21
1)( a r c c o s
x
x

21
)( a r c c o s
x
dxxd

21
1)( a rct a n
x
x

21)( a rct a n x
dxxd
21
1)co t( a rc
x
x
2
1
)co t( a rc
x
dxxd

二、导数法则和微分法则
(1) (u?v)?=uv? d(u?v)=du?dv
(2) (uv)?=u?v+uv? d(uv)=vdu+udv
(Cv)?=Cv? d(Cv)=Cdv
2)( )3( v
vuvu
v
u
2)( v
u d vvd u
v
ud
2)
1(
v
v
v

2)
1(
v
dv
vd
(4) yx?=yu?ux? dy=yu?ux?dx