设z=(x,y)由方程x/z=ln(z/y)所确定,求Zx , Zy

Question

设z=(x,y)由方程x/z=ln(z/y)所确定,求Zx , Zy
(求的Zx,Zy中,x,y是下角标)

Answer 1

x/Z = ln(Z/y),

x = Z[lnZ - lny],

等式两边同时对x求偏导，

1 = Zx[lnZ - lny] + Z[Zx/Z],

1 = Zx[lnZ - lny + 1],

Zx = 1/[lnZ - lny + 1].

等式两边同时对y求偏导，

0 = Zy[lnZ - lny] + Z[Zy/Z - 1/y],

Z/y = Zy[lnZ - lny + 1],

Zy = Z/[y(lnZ - lny + 1)].

Answer 2

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