隐函数求混合偏导设 x^2+2y^2+3z^2=16,求 d^2z/dxdy

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隐函数求混合偏导设x^2+2y^2+3z^2=16,求d^2z/dxdy隐函数求混合偏导设x^2+2y^2+3z^2=16,求d^2z/dxdy隐函数求混合偏导设x^2+2y^2+3z^2=16,求d

隐函数求混合偏导设 x^2+2y^2+3z^2=16,求 d^2z/dxdy
隐函数求混合偏导
设 x^2+2y^2+3z^2=16,求 d^2z/dxdy

隐函数求混合偏导设 x^2+2y^2+3z^2=16,求 d^2z/dxdy
d/dy:4y+6z dz/dy=0------------(1)
dz/dy=-2y/(3z)
d/dx:
2x+6z dz/dx=0
dz/dx=-x/(3z)
d(1)/dx:
6z d^2z/dxdy+6dz/dy dz/dx=0
d^2z/dxdy= -(1/z) (dz/dy dz/dx)
=-(1/z)(-2y/(3z))(-x/(3z))=(-2/9)(xy/(z^3))