已知函数z=f(x,y)由方程x2+2y2+3z2+xy-z-9=0确定,求αz/αx,αz/αy

Question

已知函数z=f(x,y)由方程x2+2y2+3z2+xy-z-9=0确定,求αz/αx,αz/αy

Answer 1

x^2+2y^2+3z^2+xy-z-9=0
求微分
2xdx+4ydy+6zdz+xdy+ydx-dz=0
(2x+y)dx+(4y+x)dy+(6z-1)dz=0
(1-6z)dz=(2x+y)dx+(4y+x)dy
dz=(2x+y)/(1-6z)*dx+(4y+x)/(1-6z)*dy
∂z/∂x=(2x+y)/(1-6z)
∂z/∂y=(4y+x)/(1-6z)