知道的回答下,x+y+z=0,x^2 + y^2 +z^2 = 1求:dy/dx,dz/dx

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知道的回答下,x+y+z=0,x^2+y^2+z^2=1求:dy/dx,dz/dx知道的回答下,x+y+z=0,x^2+y^2+z^2=1求:dy/dx,dz/dx知道的回答下,x+y+z=0,x^2

知道的回答下,x+y+z=0,x^2 + y^2 +z^2 = 1求:dy/dx,dz/dx
知道的回答下,
x+y+z=0,x^2 + y^2 +z^2 = 1
求:dy/dx,dz/dx

知道的回答下,x+y+z=0,x^2 + y^2 +z^2 = 1求:dy/dx,dz/dx
对两个式子同时对x求导,即
1+dy/dx+dz/dx=0 (1)
2x+2ydy/dx+2zdz/dx=0 (2)
把dy/dx,dz/dx 当做两个未知数,解这个二元一次方程组
(1)*2y-(2),即
2y-2x+(2y-2z)dz/dx=0
所以dz/dx=(x-y)/(y-z)
同理可得dy/dx=(x-z)/(z-y)

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