Re: [微分] 反函數之導數
※ 引述《grant310657 (風火輪)》之銘言：
: f(X)=X sinX
: -1
: 求[Dx (f )(X)]
: X=PI/2
: 答案是1
-1
令 g = f (x) , 則 g(f(x)) = x
1
(g'(f(x)))(f'(x)) = 1 => g'(f(x)) = -------
f'(x)
π π
令 f(x) = (x)(sin(x)) = --- , 則 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
--
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03/29 17:28, , 1F
03/29 17:28, 1F
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