设y=(x²-2)/(x²-x-2),求y的n阶导数
人气：415 ℃ 时间：2020-02-03 15:17:43
解答
y = 1 + [x/(x+1)(x-2)]= 1 + (x-2)^(-1) - [1/(x+1)(x-2)]= 1 + (x-2)^(-1) - (1/3)[1/(x-2)] + (1/3)[1/(x+1)]= 1 + (2/3)·(x-2)^(-1) + (1/3)·(x+1)^(-1)∴y的n阶导数 = (2/3)·(-1)^n·n!·(x-2)^(-n-1) + (1/...
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