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Proof in partial derivative

  1. Mar 19, 2009 #1
    1. The problem statement, all variables and given/known data
    consider a function F : R^2 [tex]\rightarrow[/tex]R^2 given as F(x,y)=(F1(x,y),F2(x,y)).Show that if F=[tex]\nabla[/tex]f for some function f : R^2[tex]\rightarrow[/tex]R,then
    (for partial derivative )
    DF1/Dy=DF2/Dx
    show that F(x,y)=(ycos(X),xsin(y))is not the gradient of a function


    2. Relevant equations



    3. The attempt at a solution
    i don't know how to set about this question
    any clue ?
     
    Last edited: Mar 19, 2009
  2. jcsd
  3. Mar 19, 2009 #2
    Last edited by a moderator: Apr 24, 2017
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