📝 题目
5.2.3 设
$$ f\left( {x,y}\right) = \left\{ \begin{matrix} \frac{{x}^{2}y}{{x}^{2} + {y}^{2}}, & {x}^{2} + {y}^{2} \neq 0, \\ 0, & {x}^{2} + {y}^{2} =
💡 答案与解析
5.2.3 (2) ${f}_{x}^{\prime }\left( {0,0}\right) = {f}_{y}^{\prime }\left( {0,0}\right) = 0$ ;
(3) ${f}_{x}^{\prime }\left( {x,y}\right) = \frac{{2x}{y}^{3}}{{\left( {x}^{2} + {y}^{2}\right) }^{2}},{f}_{y}^{\prime }\left( {x,y}\right) = \frac{{x}^{2}\left( {{x}^{2} - {y}^{2}}\right) }{{\left( {x}^{2} + {y}^{2}\right) }^{2}}$ .