∵1/(x²-4x+3)=(1/2)[1/(x-3)-1/(x-1)]
又[1/(x-a)]的n阶导数=(-1)^n*n!/(x-a)^(n+1)
∴[1/(x-3)]的n阶导数=(-1)^n*n!/(x-3)^(n+1)
[1/(x-1)]的n阶导数=(-1)^n*n!/(x-1)^(n+1)
故[1/(x²-4x+3)]的n阶导数=(1/2){[1/(x-3)]的n阶导数-[1/(x-1)]的n阶导数}
=(1/2)[(-1)^n*n!/(x-3)^(n+1)-(-1)^n*n!/(x-1)^(n+1)]
=[(-1)^n*n!/2]*[1/(x-3)^(n+1)-1/(x-1)^(n+1)].
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024