求高阶导数：y=(1+x^2)/(1-x^2)_数学解答

求高阶导数：y=(1+x^2)/(1-x^2)

人气：350 ℃　时间：2020-07-14 00:33:31

解答

y=(1+x^2)/(1-x^2)
= [2-(1-x^2)]/(1-x^2)
= 2/(1-x^2) - 1
= 1/(1+x) + 1/(1-x) - 1
= 1/(x+1) - 1/(x-1) - 1
y(n) = (-1)^n*n!*1/(x+1)^(n+1) - (-1)^n*n!*1/(x-1)^(n+1)
= (-1)^n*n!*[ 1/(x+1)^(n+1) - 1/(x-1)^(n+1) ]