设 $f(u, v)$ 有二阶连续偏导数，$z=f(x, x y)$ ，则 $\frac{\partial^2 z}{\partial x \partial y}=()$ 。
A. $x f_{12}^{\prime \prime}+x y f_{22}^{\prime \prime}+f_2^{\prime}$
B. $f_{12}^{\prime \prime}+x y f_{22}^{\prime \prime}+f_2^{\prime}$
C. $x f_{12}^{\prime \prime}+x y f_{22}^{\prime \prime}$
D. $x f_{12}^{\prime \prime}+y f_{22}^{\prime \prime}+f_2^{\prime}$