www.fltk.net > x分之ArCtAnx的导数

x分之ArCtAnx的导数

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

x=tany 对x求导1=y'*sec^2y=>y'=1/sec^2y=1/(tan^2y+1)=1/(x^2+1)

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

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

一种是根据定义去证明,另一种是利用反函数的导数去证明!

(1+X平方的和)的平方分之2-4Xarctanx

=1

由反函数求导公式函数x=φ(y)的反函数y=f(x)的导数为1/φ'(y)故: (arctanx)'=1/(tany)′=[(siny)/(cosy)]′由导数的基本运算公式得[(siny)/(cosy)]′=1/(cosy)则(arctanx)'=(cosy)=(cosy)/1=(cosy)/(siny)+(cosy)=1/1+x希望能够帮到您lol(*^^*)

y'=5cos5x-3(cosx)^2sinx

∫arctanxdx=xarctanx-∫xdarctanx=xarctanx-∫x/(1+x)dx=xarctanx-1/2ln(1+x)+c所以是:xarctanx-1/2ln(1+x)+c的导数.

网站地图

All rights reserved Powered by www.fltk.net

copyright ©right 2010-2021。
www.fltk.net内容来自网络,如有侵犯请联系客服。zhit325@qq.com