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]. $\frac{\partial z}{\partial x}$ $=$ $\lim_{\Delta \rightarrow x}$ $\frac{f(x, y + \Delta y) – f(x, y)}{\Delta x}$[B]. $\frac{\partial z}{\partial x}$ $=$ $\lim_{\Delta \rightarrow x}$ $\frac{f(x + \Delta x, y) + f(x, y)}{\Delta x}$
[C]. $\frac{\partial z}{\partial x}$ $=$ $\lim_{\Delta \rightarrow x}$ $\frac{f(x + \Delta x, y) – f(x, y)}{f(x, y)}$
[D]. $\frac{\partial z}{\partial x}$ $=$ $\lim_{\Delta \rightarrow x}$ $\frac{f(x + \Delta x, y) – f(x, y)}{x}$
$\frac{\partial \textcolor{red}{z}}{\partial \textcolor{orange}{x}}$ $=$ $\lim_{\textcolor{yellow}{\Delta} \rightarrow \textcolor{orange}{x}}$ $\frac{f(\textcolor{orange}{x} + \textcolor{yellow}{\Delta} \textcolor{orange}{x}, \textcolor{cyan}{y}) \textcolor{yellow}{-} f(\textcolor{orange}{x}, \textcolor{cyan}{y})}{\textcolor{yellow}{\Delta} \textcolor{orange}{x}}$