二元复合函数求导法则（B012）

问题

已知函数 $F(x, y)$ $=$ $0$, 若 $F_y^{\prime}$ $\neq$ $0$, 则 $\frac{\mathrm{d} y}{\mathrm{~d} x}=$ $?$

选项

[A].   $\frac{\mathrm{d} y}{\mathrm{~d} x}=$ $\frac{F_{x}^{\prime}(x, y)}{F_{y}^{\prime}(x, y)}$

[B].   $\frac{\mathrm{d} y}{\mathrm{~d} x}=$ $-\frac{F_{x}^{\prime}(x, y)}{F_{y}^{\prime}(x, y)}$

[C].   $\frac{\mathrm{d} y}{\mathrm{~d} x}=$ $\frac{F_{y}^{\prime}(x, y)}{F_{x}^{\prime}(x, y)}$

[D].   $\frac{\mathrm{d} y}{\mathrm{~d} x}=$ $-\frac{F_{y}^{\prime}(x, y)}{F_{x}^{\prime}(x, y)}$

   答 案   

$\frac{\mathrm{d} y}{\mathrm{~d} x}=$ $-\frac{F_{x}^{\prime}(x, y)}{F_{y}^{\prime}(x, y)}$