作者goshfju (cola)
看板trans_math
標題Re: [考古] 91交大
時間Sun May 20 23:41:17 2007
※ 引述《kusorz (^~^)》之銘言：
: suppose the f is one to one and f(1)=2,f(2)=3,f'(1)=1,f'(2)=3,f'(3)=5
: find (f^-1)'(2)=?
-1
f(1)=2 , f (2)=1
-1 -1
(f )'(2) = 1/f'(f (2)) = 1/f'(1) = 1/1 = 1
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◆ From: 59.112.84.195
1F：推 MrTang:我算1/2...真糗~~~ 61.228.163.30 05/21 01:08
2F：→ MrTang:能問一下f'(2)的反函數~下一步是怎麼來的. 61.228.163.30 05/21 01:09
3F：推 MrTang:想不太出來 61.228.163.30 05/21 01:15
4F：→ goshfju:你是指反函數微分的公式嗎? 59.112.84.195 05/21 01:26
5F：→ goshfju:其實上面3261篇就有板友貼了 你可以去參考 59.112.84.195 05/21 01:27
6F：→ goshfju: y=f^-1 => f(y)=x => f(f^-1(x))=x 59.112.84.195 05/21 01:29
7F：→ goshfju:上式對x微分 f'(f^-1(x))*(f^-1)'(x)=1 59.112.84.195 05/21 01:30
8F：→ goshfju:(f^-1)'(x) = 1 / f'(f^-1(x)) 59.112.84.195 05/21 01:30
9F：→ MrTang:謝謝~ 61.228.155.248 05/21 23:53