y=x/x^2-3x+2的n阶导数
问题描述：
y=x/x^2-3x+2的n阶导数
答
y=x/(x-1)(x-2)
=1/(x-1)+2/(x-2)(x-1)
=1/(x-1)+2/(x-2)-2/(x-1)
=2/(x-2)-1/(x-1)
y'=-2(x-2)^(-2)+(x-1)^(-2)
y''=4(x-2)^(-3)-2(x-1)^(-3)
y'''=-12(x-2)^(-4)+6(x-1)^(-4)
.
y(n)=2*(-1)^n*n!*(x-2)^(-n-1)+(-1)^(n+1)*n!*(x-1)^(-n-1)