基本初等函数的导数公式推导

问题描述:

基本初等函数的导数公式推导

C'=0(C为常数函数
(x^n)'= nx^(n-1) (n∈Q*);熟记1/X的导数
(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)
(e^x)' = e^x
(Inx)' = 1/x
(logax)' =(1/x)*logae
①(u±v)'=u'±v'   ②(uv)'=u'v+uv'   ③(u/v)'=(u'v-uv')/ v^2