y=x/(x^2-3x+2),求y的n阶导数，求详细过程

---

y=x/(x^2-3x+2)
=2/亏漏(x-2) -1/(x-1)
故y的n阶导数就等于2/(x-2)与1/(x-1)的n阶掘肆导数之差，
而
[2/判空轿(x-2)]′= -2(x-2)^(-2)
[2/(x-2)]′′=2*(-1)*(-2)*(x-2)^(-3)
[2/(x-2)]′′′=2*(-1)*(-2)*(-3)*(x-2)^(-4)
......
[2/(x-2)]^n=2*(-1)(-2)(-3)....(-n) *(x-2)^(-n-1)
同理
1/(x-1)的n阶导数= (-1)(-2)(-3)....(-n) *(x-1)^(-n-1)

所以
y的n阶导数
=2*(-1)(-2)(-3)....(-n) *(x-2)^(-n-1) - (-1)(-2)(-3)....(-n) *(x-1)^(-n-1)
=(-1)(-2)(-3)....(-n) *[2(x-2)^(-n-1) -(x-1)^(-n-1)]

---

y=x/配孝(x^2-3x+2)
=x/(x-1)(x-2)=2/(x-2)-1/(x-1)
由于1/(x-2)的n阶导数=(-1)^n*n!/(x-2)^(n+1)
1/(x-1)的n阶导数=(-1)^n*n!/胡简(x-1)^(n+1)
所裤卖裤以：y的n阶导数
=2(-1)^n*n!/(x-2)^(n+1)-(-1)^n*n!/(x-1)^(n+1)
=(-1)^n*n![2/(x-2)^(n+1)-1/(x-1)^(n+1)]

---