作者LuisSantos ( )
看板trans_math
标题Re: [微分] 反函数之导数
时间Sat Mar 28 17:18:31 2009
※ 引述《grant310657 (风火轮)》之铭言：
: f(X)=X sinX
: -1
: 求[Dx (f )(X)]
: X=PI/2
: 答案是1
-1
令 g = f (x) , 则 g(f(x)) = x
1
(g'(f(x)))(f'(x)) = 1 => g'(f(x)) = -------
f'(x)
π π
令 f(x) = (x)(sin(x)) = --- , 则 x = ---
2 2
f'(x) = sin(x) + (x)(cos(x))
π π
f'(---) = 1 + (---)(0) = 1
2 2
-1
[Dxf (x)]
x = π/2
1 1
= g'(π/2) = ---------- = --- = 1
f'(π/2) 1
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 140.119.129.128
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