f(x,y)=xy/(x^2+y^2) x^2+y^2 不=(0,0)f(x,y)=0 x^2+y^2 =(0,0)在(0,0)对x的偏导数为多少
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f(x,y)=xy/(x^2+y^2)x^2+y^2不=(0,0)f(x,y)=0x^2+y^2=(0,0)在(0,0)对x的偏导数为多少f(x,y)=xy/(x^2+y^2)x^2+y^2不=(0,
f(x,y)=xy/(x^2+y^2) x^2+y^2 不=(0,0)f(x,y)=0 x^2+y^2 =(0,0)在(0,0)对x的偏导数为多少
f(x,y)=xy/(x^2+y^2) x^2+y^2 不=(0,0)
f(x,y)=0 x^2+y^2 =(0,0)
在(0,0)对x的偏导数为多少
f(x,y)=xy/(x^2+y^2) x^2+y^2 不=(0,0)f(x,y)=0 x^2+y^2 =(0,0)在(0,0)对x的偏导数为多少
由偏导数定义,可知函数f(x,y)在(0,0)对x的偏导数为:
lim(⊿x->0) [f(0+⊿x,0)-f(0,0)]/⊿x .
因为,
f(0,0) = 0 ,
f(⊿x,0) = (⊿x·0) / [(⊿x)²+0²] = 0 ;
所以,
lim(⊿x->0) [f(0+⊿x,0)-f(0,0)]/⊿x = 0 ;
即:f(x,y)在(0,0)对x的偏导数为 0 .
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