fnhp.net
当前位置:首页 >> E的ArCtAnx的二阶导数 >>

E的ArCtAnx的二阶导数

要点:链式求导法则,e^x的导数,arctanx的导数

y=tanx y'=secx 所以y''=2secx*(secx)'=2secx*secxtanx=2secxtanx

你好!y' = e^arctanx + (x-1) e^(arctanx) /(1+x^2) = e^arctanx [ (x+x^2) / (1+x^2) ]如有疑问可追问

分部求导Y'=(x-1)' e^arctanx+(x-1)(e^arctanx)' =-e^arctanx+(x-1)e^arctanx (arctanx )'=-e^arctanx+(1/x) (x-1)e^arctanx =(x-1) /x e^arctanx -e^arctanx=(1/x-2)e^arctanx

y'=arctanx+x/(1+x^2) y''=2/(1+x^2)-2*x^2/(1+x^2)^2

f(x)=x^2*arctanxf'(x)=x*arctanx+x^2/(1+x^2)=x*arctanx+1-1/(1+x^2)f''(x)=arctanx+x/(1+x^2)+2x/(1+x^2)^2

y'=(2-x^2)' *arctanx +(2-x^2) *(arctanx)'= -2x *arctanx +(2-x^2) /(1+x^2)=-2x *arctanx -1 + 3/(1+x^2)那么再继续求导得到二阶导数y"= -2arctanx -2x/(1+x^2) -3/(1+x^2)^2 *(1+x^2)'= -2arctanx -2x/(1+x^2) -3/(1+x^2)^2 *2x= -2arctanx -2x/(1+x^2) - 6x/(1+x^2)^2

是这样来的y`=e^(arctanx)/(1+x)y``=[(e^(arctanx)`(1+x)-e^(arctanx)(1+x)`]/(1+x)=[(e^(arctanx)-e^(arctanx)(2x)]/(1+x)=e^(arctanx)(1-2x)/(1+x)=-2(arctanx)(x-1/2)/(1+x)

^y=(1+x)e^y则有:y'=y'e^y+e^y+xy'e^y.则y'=y'(1+x)e^y+e^y.则y'=e^y/(1-(1+x)e^y)=e^y/(1-y).而y''=[y'e^y(1-y)-e^y(-y')]/(1-y)^2=[y'e^y-y'ye^y+y'e^y]/(1-y)^2=y'(2-y)e^y/(1-y)^2.则y''=(2-y)e^2y/(1-y)^3.

网站首页 | 网站地图
All rights reserved Powered by www.fnhp.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com