x=(y,z),y=(x,z),z=z(x,y)是F(x,y,z)=0所确定的具连续偏导数的函数,证明x对y偏导*y对z偏导*z对x偏导=-1
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![x=(y,z),y=(x,z),z=z(x,y)是F(x,y,z)=0所确定的具连续偏导数的函数,证明x对y偏导*y对z偏导*z对x偏导=-1](/uploads/image/z/7259976-0-6.jpg?t=x%3D%28y%2Cz%29%2Cy%3D%28x%2Cz%29%2Cz%3Dz%28x%2Cy%29%E6%98%AFF%28x%2Cy%2Cz%29%3D0%E6%89%80%E7%A1%AE%E5%AE%9A%E7%9A%84%E5%85%B7%E8%BF%9E%E7%BB%AD%E5%81%8F%E5%AF%BC%E6%95%B0%E7%9A%84%E5%87%BD%E6%95%B0%2C%E8%AF%81%E6%98%8Ex%E5%AF%B9y%E5%81%8F%E5%AF%BC%2Ay%E5%AF%B9z%E5%81%8F%E5%AF%BC%2Az%E5%AF%B9x%E5%81%8F%E5%AF%BC%3D-1)
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x=(y,z),y=(x,z),z=z(x,y)是F(x,y,z)=0所确定的具连续偏导数的函数,证明x对y偏导*y对z偏导*z对x偏导=-1
x=(y,z),y=(x,z),z=z(x,y)是F(x,y,z)=0所确定的具连续偏导数的函数,证明x对y偏导*y对z偏导*z对x偏导=-1
x=(y,z),y=(x,z),z=z(x,y)是F(x,y,z)=0所确定的具连续偏导数的函数,证明x对y偏导*y对z偏导*z对x偏导=-1
x=f(y,z)时
δF/δy=F'1*δx/δy+F'2=0
即:δx/δy=-F'2/F'1
同理:δy/δz=-F'3/F'2,δz/δx=-F'1/F'3
故(δx/δy)*(δy/δz)*(δz/δx)
=(-F'2/F'1)*(-F'3/F'2)*(-F'1/F'3)=-1
(x+y-z)(x-y+z)=
X+Y+Z=?
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