函数z=f(x,y)由方程xy+yz+zx=1所确定,求fxy" .
人气:299 ℃ 时间:2020-05-28 02:41:22
解答
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
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