F(x,y,z)=0,证明:∂z/∂x*∂x/∂y*∂y/∂z=-1怎么证明啊,
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![F(x,y,z)=0,证明:∂z/∂x*∂x/∂y*∂y/∂z=-1怎么证明啊,](/uploads/image/z/10189598-14-8.jpg?t=F%28x%2Cy%2Cz%29%3D0%2C%E8%AF%81%E6%98%8E%3A%26%238706%3Bz%2F%26%238706%3Bx%2A%26%238706%3Bx%2F%26%238706%3By%2A%26%238706%3By%2F%26%238706%3Bz%3D-1%E6%80%8E%E4%B9%88%E8%AF%81%E6%98%8E%E5%95%8A%2C)
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F(x,y,z)=0,证明:∂z/∂x*∂x/∂y*∂y/∂z=-1怎么证明啊,
F(x,y,z)=0,证明:∂z/∂x*∂x/∂y*∂y/∂z=-1
怎么证明啊,
F(x,y,z)=0,证明:∂z/∂x*∂x/∂y*∂y/∂z=-1怎么证明啊,
解析:
两边对x求偏导,得
Fx+Fz*∂z/∂x=0
所以:∂z/∂x=-Fx/Fz
同理可得
∂x/∂y=-Fy/Fx
∂y/∂z=-Fz/Fy
所以
∂z/∂x*∂x/∂y*∂y/∂z=-Fx/Fz*-Fy/Fx*-Fz/Fy=-1