设z=f(x,y)是由方程式3x^2+2y^2+z^2-2xyz=0确定的函数,求az/ax,az/ay

问题描述:

设z=f(x,y)是由方程式3x^2+2y^2+z^2-2xyz=0确定的函数,求az/ax,az/ay

设F(x,y,z)=3x^2+2y^2+z^2-2xyz
F’z=-2xy+2,F‘x=3^2-2yz,F'y=2^2-2xz
az/ax=-F’z/F‘x=(xy-1)/(3-yz)
az/ay=-F’z/F'y=(xy-1)/(2-xz)