求y的导函数
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解决时间 2021-11-11 01:03
- 提问者网友：不要迷恋哥
- 2021-11-10 20:08
求y的导函数
最佳答案
- 五星知识达人网友：摆渡翁
- 2021-11-10 20:32
y
= 1/(x^2-2x-3)
= 1/[(x-3)(x+1)]
= (1/4) [1/(x-3) -1/(x+1)]
y^(n)(x) = (1/4)(-1)^n. (n!). [1/(x-3)^(n+1) -1/(x+1)^(n+1) ]追问哪来的1/4啊追答1/(x-3) -1/(x+1)
=[(x+1)-(x-3)]/[(x+1)(x-3)]
=4/[(x+1)(x-3)]
=>
(1/4) { 1/[(x-3)(x+1)] } = 1/[(x+1)(x-3)]
= 1/(x^2-2x-3)
= 1/[(x-3)(x+1)]
= (1/4) [1/(x-3) -1/(x+1)]
y^(n)(x) = (1/4)(-1)^n. (n!). [1/(x-3)^(n+1) -1/(x+1)^(n+1) ]追问哪来的1/4啊追答1/(x-3) -1/(x+1)
=[(x+1)-(x-3)]/[(x+1)(x-3)]
=4/[(x+1)(x-3)]
=>
(1/4) { 1/[(x-3)(x+1)] } = 1/[(x+1)(x-3)]
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