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)'=hcoshx (coshx)'=-hsinhx
(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)' =(xlna)^(-1),(a>0且a不等于1) (x^1/2)'=[2(x^1/2)]^(-1)
(1/x)'=-x^(-2) .y=c(c为常数) y'=0 .y=x^n
y'=nx^(n-1) .y=a^x
y'=a^xlna y=e^x
y'=e^x y=lnx
y'=1/x .y=sinx
y'=cosx .y=cosx
y'=-sinx .y=tanx
y'=1/cos^2x .y=cotx
y'=-1/sin^2x .y=arcsinx
y'=1/√1-x^2 .y=arccosx
y'=-1/√1-x^2 .y=arctanx
y'=1/1+x^2 .y=arccotx
y'=-1/1+x^2 按照公式代就行了
y=f(x)=c (c为常数),则f'(x)=0
f(x)=x^n (n不等于0) f'(x)=nx^(n-1) (x^n表示x的n次方) f(x)=sinx
f'(x)=cosx f(x)=cosx f'(x)=-sinx f(x)=a^x
f'(x)=a^xlna(a>0且a不等于1,x>0) f(x)=e^x f'(x)=e^x
f(x)=logaX f'(x)=1/xlna (a>0且a不等于1,x>0)
f(x)=lnx f'(x)=1/x (x>0)
f(x)=tanx f'(x)=1/cos^2 x
f(x)=cotx f'(x)=- 1/sin^2 x
导数运算法则如下
(f(x)+/-g(x))'=f'(x)+/- g'(x) (f(x)g(x))'=f'(x)g(x)+f(x)g'(x)
(g(x)/f(x))'=(f(x)'g(x)-g(x)f'(x))/(f(x))^2
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