偏导数的值
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偏导数的值
关键是arctan(x+y)/(x-y)的导数,
设u=(x+y)/(x-y)
u'x=-2y(x-y)^2
所以[arctan(x+y)/(x-y)]'x=[1/(1+u^2)]*(u'x)=-y/(x^2+y^2)
f'x(x,y)=2x-y/(x^2+y^2)
所以f'x(1,1)=3/2
偏导数的值
关键是arctan(x+y)/(x-y)的导数,
设u=(x+y)/(x-y)
u'x=-2y(x-y)^2
所以[arctan(x+y)/(x-y)]'x=[1/(1+u^2)]*(u'x)=-y/(x^2+y^2)
f'x(x,y)=2x-y/(x^2+y^2)
所以f'x(1,1)=3/2