y=x⼀x^2-3x+2的n阶导数

2024-12-16 00:40:39
推荐回答(1个)
回答1:

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)