已知可微函数 $f(u, v)$ 满足
$$
\frac{\partial f(u, v)}{\partial u}-\frac{\partial f(u, v)}{\partial v}=2(u-v) e^{-(u+v)}
$$
且 $f(u, 0)=u^2 e^{-u}$.
(1) 记 $g(x, y)=f(x, y-x)$ ，求 $\frac{\partial g(x, y)}{\partial x}$.
(2) 求 $f(u, v)$ 的表达式和极值.
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$\text{B.}$
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