问题
若已知函数 $f(x, y, z)$ 在点 $\left(x_{0}, y_{0}, z_{0}\right)$ 处可微, 且 $(\cos \alpha, \cos \beta, \cos \gamma)$ 是 $\boldsymbol{l}$ 方向的方向余弦.那么，该函数在该点沿任何方向 $\boldsymbol{l}$ 的方向导数 $\left.\frac{\partial f}{\partial \boldsymbol{l}}\right|_{\left(x_{0}, y_{0}, z_{0}\right)}$ 都存在，则 $\left.\frac{\partial f}{\partial \boldsymbol{l}}\right|_{\left(x_{0}, y_{0}, z_{0}\right)}$ $=$ $?$
选项
[A]. $\left.\frac{\partial f}{\partial \boldsymbol{l}}\right|_{\left(x_{0}, y_{0}, z_{0}\right)}$ $=$ $f_{x}\left(x_{0}, y_{0}, z_{0}\right) \cos \alpha$ $+$ $f_{y}\left(x_{0}, y_{0}, z_{0}\right) \cos \beta$ $+$ $f_{z}\left(x_{0}, y_{0}, z_{0}\right) \cos \gamma$[B]. $\left.\frac{\partial f}{\partial \boldsymbol{l}}\right|_{\left(x_{0}, y_{0}, z_{0}\right)}$ $=$ $f_{x}\left(x_{0}, y_{0}, z_{0}\right) \cos \gamma$ $+$ $f_{y}\left(x_{0}, y_{0}, z_{0}\right) \cos \beta$ $+$ $f_{z}\left(x_{0}, y_{0}, z_{0}\right) \cos \alpha$
[C]. $\left.\frac{\partial f}{\partial \boldsymbol{l}}\right|_{\left(x_{0}, y_{0}, z_{0}\right)}$ $=$ $f_{x}\left(x_{0}, y_{0}, z_{0}\right) \cos \alpha$ $-$ $f_{y}\left(x_{0}, y_{0}, z_{0}\right) \cos \beta$ $-$ $f_{z}\left(x_{0}, y_{0}, z_{0}\right) \cos \gamma$
[D]. $\left.\frac{\partial f}{\partial \boldsymbol{l}}\right|_{\left(x_{0}, y_{0}, z_{0}\right)}$ $=$ $f_{x}\left(x_{0}, y_{0}, z_{0}\right) \sin \alpha$ $+$ $f_{y}\left(x_{0}, y_{0}, z_{0}\right) \sin \beta$ $+$ $f_{z}\left(x_{0}, y_{0}, z_{0}\right) \sin \gamma$
$\left.\frac{\partial f}{\partial \boldsymbol{l}}\right|_{\left(x_{0}, y_{0}, z_{0}\right)}$ $=$ $f_{x}\left(x_{0}, y_{0}, z_{0}\right) \cos \alpha$ $+$ $f_{y}\left(x_{0}, y_{0}, z_{0}\right) \cos \beta$ $+$ $f_{z}\left(x_{0}, y_{0}, z_{0}\right) \cos \gamma$