若二元函数 $f(x, y)$ 存在二阶连续偏导数, 且满足 $f(x, y)=-f(y, x)$, 则下列结论中, 错误的是
A. $f_{11}^{\prime \prime}(x, y)=f_{22}^{\prime \prime}(x, y)$.
B. $f_{11}^{\prime \prime}(x, y)=-f_{22}^{\prime \prime}(y, x)$.
C. $f_{12}^{\prime \prime}(x, y)=f_{21}^{\prime \prime}(x, y)$.
D. $f_{12}^{\prime \prime}(x, y)=-f_{21}^{\prime \prime}(y, x)$.