简单计算一下即可，详情如图所示
z=x^2+y^2①x^2+2y^2+2z^2=20。②①+②，得z+y^2+2z^2=20,微分得dz+2ydy+4zdz=0,2ydy=-(4z+1)dz,所以dy/dz=-(4z+1)/(2y).①*2+②，得2z-x^2+2z^2=20,微分得2dz-2xdx+4zdz=0,(2z+1)dz=xdx,所以dz/dx=x/(2z+1).
