Find f^n(x) for following functions f(x)：
f(x) = 1 / ( 1 - x^2 )
個答案係：
1 1 ( - 1 )^n
--- n ! [ ------------------ + ------------------- ]
2 ( 1 - x )^(n+1) ( 1 + x )^(n+1)
請各位高手幫助一下！！謝謝！！
高階導數 (higher derivative) 的問題！！
2008-09-24 6:55 am
回答 (1)
2008-09-24 8:29 am
✔ 最佳答案
Consider 1/(1-x^2)=1/(1+x)(1-x)
=1/2[1/(1+x) + 1/(1-x)]
Since d^n/dx^n[1/(1+x)]=n!(-1)^n[1/(1+x)^(n+1)]
therefore,
f^(n)(x) ={1/2[1/(1+x) + 1/(1-x)]}^(n)
=1/2[n!(-1)^n/(1+x)^(n+1) + n!(-1)^2n/(1-x)^(n+1)]
=n!/2[1/(1-x)^(n+1)+!(-1)^n/(1+x)^(n+1)]
收錄日期: 2021-04-13 21:57:41
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080923000051KK02533