问题
已知函数 $F(x, y, z)$ $=$ $0$, 若 $F_{z}^{\prime}$ $\neq$ $0$, 则 $\frac{\partial z}{\partial x}$ $=$ $?$, $\frac{\partial z}{\partial y}$ $=$ $?$选项
[A]. $\frac{\partial z}{\partial x}$ $=$ $-$ $\frac{F_{x}^{\prime}(x, y, z)}{F_{z}^{\prime}(x, y, z)}$, $\frac{\partial z}{\partial y}$ $=$ $-$ $\frac{F_{y}^{\prime}(x, y, z)}{F_{z}^{\prime}(x, y, z)}$[B]. $\frac{\partial z}{\partial x}$ $=$ $-$ $\frac{F_{z}^{\prime}(x, y, z)}{F_{x}^{\prime}(x, y, z)}$, $\frac{\partial z}{\partial y}$ $=$ $-$ $\frac{F_{z}^{\prime}(x, y, z)}{F_{y}^{\prime}(x, y, z)}$
[C]. $\frac{\partial z}{\partial x}$ $=$ $-$ $\frac{F_{x}^{\prime}(x, y, z)}{F_{z}(x, y, z)}$, $\frac{\partial z}{\partial y}$ $=$ $-$ $\frac{F_{y}^{\prime}(x, y, z)}{F_{z}(x, y, z)}$
[D]. $\frac{\partial z}{\partial x}$ $=$ $\frac{F_{x}^{\prime}(x, y, z)}{F_{z}^{\prime}(x, y, z)}$, $\frac{\partial z}{\partial y}$ $=$ $\frac{F_{y}^{\prime}(x, y, z)}{F_{z}^{\prime}(x, y, z)}$
$\frac{\partial z}{\partial x}$ $=$ $-$ $\frac{F_{x}^{\prime}(x, y, z)}{F_{z}^{\prime}(x, y, z)}$, $\frac{\partial z}{\partial y}$ $=$ $-$ $\frac{F_{y}^{\prime}(x, y, z)}{F_{z}^{\prime}(x, y, z)}$