用对数求导法求导:y=[x*(x^2+1)/(x-1)^2]^1/3

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 12:53:20
用对数求导法求导:y=[x*(x^2+1)/(x-1)^2]^1/3

用对数求导法求导:y=[x*(x^2+1)/(x-1)^2]^1/3
用对数求导法求导:y=[x*(x^2+1)/(x-1)^2]^1/3

用对数求导法求导:y=[x*(x^2+1)/(x-1)^2]^1/3
等式两边取对数有:lny=1/3ln[x*(x^2+1)/(x-1)^2]
化简得3lny=lnx+ln(x^2+1)-2ln|x-1|
两边求导3y'/y=1/x+2x/(x^2+1)-2/(x-1)
y'=1/3*y[1/x+2x/(x^2+1)-2/(x-1)]
=1/3*[1/x+2x/(x^2+1)-2/(x-1)]*[x*(x^2+1)/(x-1)^2]^1/3