Question

高中导数的基本公式

Answer 1

① C'=0(C为常数函数)

② (x^n)'= nx^(n-1) (n∈Q*)；熟记1/X的导数

③ (sinx)' = cosx

(cosx)' = - sinx

(tanx)'=1/(cosx)^2=(secx)^2=1+(tanx)^2

-(cotx)'=1/(sinx)^2=(cscx)^2=1+(cotx)^2

(secx)'=tanx·secx

(cscx)'=-cotx·cscx

(arcsinx)'=1/(1-x^2)^1/2

(arccosx)'=-1/(1-x^2)^1/2

(arctanx)'=1/(1+x^2)

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

(arcsecx)'=1/(|x|(x^2-1)^1/2)

(arccscx)'=-1/(|x|(x^2-1)^1/2)

④(sinhx)'=coshx

(coshx)'=sinhx

(tanhx)'=1/(coshx)^2=(sechx)^2

(coth)'=-1/(sinhx)^2=-(cschx)^2

(sechx)'=-tanhx·sechx

(cschx)'=-cothx·cschx

(arsinhx)'=1/(x^2+1)^1/2

(arcoshx)'=1/(x^2-1)^1/2

(artanhx)'=1/(x^2-1) (|x|<1)

(arcothx)'=1/(x^2-1) (|x|>1)

(arsechx)'=1/(x(1-x^2)^1/2)

(arcschx)'=1/(x(1+x^2)^1/2)

⑤ (e^x)' = e^x

(a^x)' = a^xlna （ln为自然对数）

(Inx)' = 1/x（ln为自然对数）

(logax)' =x^(-1)logae(a>0且a不等于1)

(x^1/2)'=[2(x^1/2)]^(-1)

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

Answer 2

常用导数公式
1.y=c(c为常数) y'=0
2.y=x^n y'=nx^(n-1)
3.y=a^x y'=a^xlna
y=e^x y'=e^x
4.y=logax y'=logae/x
y=lnx y'=1/x
5.y=sinx y'=cosx
6.y=cosx y'=-sinx
7.y=tanx y'=1/cos^2x
8.y=cotx y'=-1/sin^2x
9.y=arcsinx y'=1/√1-x^2
10.y=arccosx y'=-1/√1-x^2
11.y=arctanx y'=1/1+x^2
12.y=arccotx y'=-1/1+x^2

Answer 3

8个
(C)'=0
(x^n)'=nx^(n-1)
(sinx)'=cosx
(cosx)'=-sinx
(e^x)'=e^x
(lnx)'=1/x
(a^x)=a^xlna
(loga(x))'=1/(xlna)

Answer 4

常用导数公式
1.y=c(c为常数) y'=0
2.y=x^n y'=nx^(n-1)
3.y=a^x y'=a^xlna
y=e^x y'=e^x
4.y=logax y'=﹙logae﹚/x
y=lnx y'=1/x
5.y=sinx y'=cosx
6.y=cosx y'=－sinx