设 $f$ 为二元可微函数, $z=y f\left(\frac{y}{x}, x y\right)$, 则 $\frac{x}{y} \cdot \frac{\partial z}{\partial x}+\frac{\partial z}{\partial y}=(\quad)$.
A. $f+2 \frac{x}{y} \cdot f_1^{\prime}$
B. $f-2 \frac{x}{y} \cdot f_1^{\prime}$
C. $f+2 x y f_2^{\prime}$
D. $f-2 x y f_2^{\prime}$