📝 题目
5.3.6 设 $z = z\left( {x,y}\right)$ 由方程 $F\left( {x + \frac{z}{y},y + \frac{z}{x}}\right) = 0$ 所确定,证明:
$$ x\frac{\partial z}{\partial x} + y\frac{\partial z}{\partial y} = z - {xy}. $$
5.3.6 设 $z = z\left( {x,y}\right)$ 由方程 $F\left( {x + \frac{z}{y},y + \frac{z}{x}}\right) = 0$ 所确定,证明:
$$ x\frac{\partial z}{\partial x} + y\frac{\partial z}{\partial y} = z - {xy}. $$