Re: [考古] 90交大
※ 引述《Ruyan (....)》之銘言：
: Suppose that eq. F(x,y,z) = 0 implicitly defines each of the three variable
: x,y,z as function of the other two:
: z = f(x,y) y = g(x,z) x = h(y,z)
: If F is differentiable and Fx , Fy , Fz are nonzero, show that
: 6z 6x 6y
: ----x----x---- = -1 6是partial 囧rz 而 ---x--- 中間的x是乘
: 6x 6y 6z
: 拜託各位高手了 ○r2
F(x,y,z) = 0
由已知條件得
6z Fx
---- = - ---- ----------(1)
6x Fz
6x Fy
---- = - ---- ----------(2)
6y Fx
6y Fz
---- = - ---- ----------(3)
6z Fy
由(1)*(2)*(3)得
6z 6x 6y Fx Fy Fz
----x----x---- = (- ----)x(- ----)x(- ----) = -1
6x 6y 6z Fz Fx Fy
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