问题
已知函数 $z$ $=$ $f(x, y)$ 在 $(x, y)$ 的某邻域内有定义，且以下选项中的极限均存在，则 $\frac{\partial z}{\partial x}$ $=$ $?$选项
[A]. $\frac{\partial z}{\partial y}$ $=$ $\lim_{\Delta \rightarrow y}$ $\frac{f(x, y + \Delta y) – f(x, y)}{\Delta x}$[B]. $\frac{\partial z}{\partial y}$ $=$ $\lim_{\Delta \rightarrow y}$ $\frac{f(x, y + \Delta y) + f(x, y)}{\Delta y}$
[C]. $\frac{\partial z}{\partial y}$ $=$ $\lim_{\Delta \rightarrow y}$ $\frac{f(x, y + \Delta y) – f(x, y)}{\Delta y}$
[D]. $\frac{\partial z}{\partial y}$ $=$ $\lim_{\Delta \rightarrow y}$ $\frac{f(x + \Delta + x, y) – f(x, y)}{\Delta x}$
$\frac{\partial \textcolor{red}{z}}{\partial \textcolor{orange}{y}}$ $=$ $\lim_{\textcolor{yellow}{\Delta} \rightarrow \textcolor{orange}{y}}$ $\frac{f(\textcolor{cyan}{x}, \textcolor{orange}{y} + \textcolor{yellow}{\Delta} \textcolor{orange}{y}) – f(\textcolor{cyan}{x}, \textcolor{orange}{y})}{\textcolor{yellow}{\Delta} \textcolor{orange}{y}}$