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设 $f(x, y)=\left\{\begin{array}{cc}\frac{x^2 y^2}{x^2+y^2}, & (x, y) \neq(0,0) \\ 0, & 0\end{array}\right.$ ，求 $f_x^{\prime}(0,0), f_y^{\prime}(0,0)$
                        
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