# Proof in partial derivative

1. Mar 19, 2009

### ak123456

1. The problem statement, all variables and given/known data
consider a function F : R^2 $$\rightarrow$$R^2 given as F(x,y)=(F1(x,y),F2(x,y)).Show that if F=$$\nabla$$f for some function f : R^2$$\rightarrow$$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