问题
若函数 $z$ $=$ $f(x,y)$ 在点 $(x, y)$ 处可微，且 $\Delta x$, $\Delta y$ 分别为自变量 $x$ 和 $y$ 的增量，$\phi$ $=$ $\sqrt{(\Delta x)^{2} + (\Delta y)^{2}}$, 则该二元函数 $z$ 的全微分 $\mathrm{d} z$ $=$ $?$选项
[A]. $\mathrm{d} z$ $=$ $\frac{\mathrm{d} z}{\mathrm{d} x}$ $\partial x$ $+$ $\frac{\mathrm{d} z}{\mathrm{d} y}$ $\partial y$ $+$ $o(\phi)$[B]. $\mathrm{d} z$ $=$ $\frac{\partial z}{\partial x}$ $\partial x$ $+$ $\frac{\partial z}{\partial y}$ $\partial y$
[C]. $\mathrm{d} z$ $=$ $\frac{\partial z}{\partial x}$ $x$ $+$ $\frac{\partial z}{\partial y}$ $y$
[D]. $\mathrm{d} z$ $=$ $\frac{\partial z}{\partial x}$ $\mathrm{d} x$ $+$ $\frac{\partial z}{\partial y}$ $\mathrm{d} y$
$\mathrm{d} z$ $=$ $\frac{\partial z}{\partial x}$ $\mathrm{d} x$ $+$ $\frac{\partial z}{\partial y}$ $\mathrm{d} y$ $\Rightarrow$
$\mathrm{d} z$ $=$ $\frac{\partial z}{\partial x}$ $\Delta x$ $+$ $\frac{\partial z}{\partial y}$ $\Delta y$