函数z=f(x y)由方程xy+yz+zx=1所确定 求fxy .

问题补充：

函数z=f(x,y)由方程xy+yz+zx=1所确定,求fxy .

答案：

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