导数公式大全 高数

基本导数公式有

(1nx)’=1/x、 (sinx)'=cosx、 (cosx)’=-sinx。

求导公式

c'=o(c为常数)

(x~a)'=ax^(a-1), a为常数且a≠0

(a ^x)'=a^x1na

(e^x)'=e x

(1ogax)’=1/(x1na), a>0且a≠1

(1nx)’=1/x

(sinx)' =cosx

(cosx)’=-sinx

(tanx)'=(secx)^2

(secx)’=secxtanx

(cotx)'=-(cscx)^2

(cscx)'=-csxcotx

(arcsinx)'=1/√(1-x^2)

(arccosx)’=-1/√(1-x ^2)

(arctanx)’=1/(1+x^2)

(arccotx)'=-1/(1+x^2)

(shx)'=chx

(chx)'=shx

(uv)'=uv'tu'v

(u+v)'=u'+v'

(u/)'=(u'v-uv')/ ^2

基本初等函数的导数表

1.y=c y' =0

2.y=a ^u y'=u a ^ ( u-1)

3.y=a 'x y'=a x1na

y=e'x y'=e~x

4.y=1oga,x y' =1oga, elx

y=1nx y'=1/x

5.y=sinx y' =cosx

6.y=cosx y'=-sinx

7.y=tanx y'=(secx)^2=1/(cosx)^2

8.y=cotx y'=-(cscx)^2=-1f(sinx)^2

9.y=arcsinx y'=1/√ (1-x^2)

10.y=arccosxy'=-1/√ (1-x^2)

11.y=arctanx y'=1/ (1+x^2)

12.y=arccotx y' =-1/(1+x^2)

13.y=sh x y'=ch x

14.y=ch x y'=sh x

15.y=thx y'=1/(chx)^2

16.y=arshxy'=1/√ (1+x^2)

17.y=ar chx y'=1/√ (x~2-1)

18.y=ar th y'=1/(1-x~2)