已知函数 $u=u(x, y), v=v(x, y)$, 满足
$$
\left\{\begin{array}{l}
x u-y v=0 \\
y x+x v=2
\end{array}\right.
$$
在 $\left(x_0, y_0, u_0, v_0\right)=(1,1,1,1)$ 的某个邻域内定义的隐函数, 求 $\frac{\partial x}{\partial x}(1,1), \frac{\partial x}{\partial y}(1,1), \frac{\partial v}{\partial x}(1,1), \frac{\partial v}{\partial y}(1,1)$.