函数z=f(x,y)由方程xy+yz+zx=1所确定,求fxy .

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z对x的偏导 xy+yz+zx=1 y＋yfx'+z+xfx'＝0 z对y的偏导 x＋z+yfy'＋xfy' ＝0 z对y的偏导 1+fx'+yfxy+fy'+xfxy =0 1+(fx'+fy')+(x+y)fxy=0 由 得:1+fx'+fy' =1-(y+z)/(x+y)-(x+z)/(x+y) =-2z/(x+y) (x+y)fxy=2z/(x+y) fxy =2z/(x+y)^2