Consider 2-D flow with ``unit'' depth.
Fluid ``volume'' ABCD at time ``t'' moves to new location A'B'C'D' at time 
For example, point A moves to A':
Similarly:
etc.
Now, for convenience we shift A'B'C'D' so that 
Then the relative motions are:
Now remember definitions of partial derivatives!
Then the above relative motions may be approximated as follows:
similarly:
From the above, it can be easily seen that:
