求X눀-Y눀=1的二阶导数,并写出详细过程,谢谢

2025-01-21 08:47:48
推荐回答(2个)
回答1:

谁对谁求导??题问不清

回答2:

y'=(x^1/y)'
  =x^(1/y)*lnx*(1/y)'+(1/y)*x^(1/y-1)
  =y*lnx*(-y'/y^2)+x^(1/y)/(xy)
  =-y'lnx/y+1/x
从而
y'(1+lnx/y)=1/x
y'=y/[x(lnx+y)]
 
y''={y'*[x(lnx+y)]-y*[x(lnx+y)]'}/[x(lnx+y)]^2
   ={y-y*[lnx+y+1+xy')]}/[x(lnx+y)]^2
   =-y*[lnx+y+y/(lnx+y)]/[x(lnx+y)]^2
   =-y*[(lnx+y)^2+y]/[x^2(lnx+y)^3]