※ 引述《jbsh (鄉民)》之銘言：
: Let F(x1,x2)be a real-valued function defined on R^2 with partial derivatives
: Fi=dF/dxi for i=1,2 .Suppose that variable v is implicitly defined as a
: function of u by the equation F(u-v,u+v)=0 .find dv/du  in terms if F1 and
: F2

  依題意: F為x1,x2之函數且 x1=u-v, x2=u+v, v是u的隱函數
          故F最終為u的函數! 圖解示意..

      F
     / \
   x1   x2
  / \  / \
 u  v  u  v
    |     |
    u     u

 以下 "@" 表偏微，原po題目打錯，應為 Fi=@F/@xi for i=1,2

 x1=u-v, x2=u+v

 F(u-v,u+v)=0 => dF/du =0

 dF/du = (@F/@x1)(@x1/@u) + (@F/@x1)(@x1/@v)(dv/du)
         + (@F/@x2)(@x2/@u) + (@F/@x2)(@x2/@v)(dv/du)

       = F1*1 + F1*(-1)*(dv/du) + F2*1 + F2*1*(dv/du)

       = (F1+F2) + (dv/du)*(F2-F1)

       = 0


 <=>   dv/du = (F1+F2)/(F1-F2)