学高数前要知道的基础

[scode type="green"]降幂[/scode]
[scode type="share"]
cos²α＝(1+cos2α）/2。

sin²α＝（1-cos2α）／2。

tan²α＝（1-cos2α）／（1+cos2α）。[/scode]
[scode type="green"]求导[/scode]
[scode type="share"]
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)=tanx f'(x)=sec^2x

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

f(x)=acrsin(x) f'(x)=1/√(1-x^2)

f(x)=acrcos(x) f'(x)=-1/√(1-x^2)

f(x)=acrtan(x) f'(x)=-1/(1+x^2)[/scode]
[scode type="green"]等差数列求和公式[/scode]
[scode type="share"]Sn=n*a1+n(n-1)d/2或Sn=n(a1+an)/2[/scode]
[scode type="green"]等差数列求和公式[/scode]
[scode type="share"]
q≠1时 Sn=a1(1-q^n)/(1-q)=(a1-anq)/(1-q)
q=1时Sn=na1
(a1为首项,an为第n项,d为公差,q 为等比)[/scode]