Question

请教数学高才生一道多元微积分的题目.

Answer 1

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