is conservative if we can find a scalar function
such that
. This is equivalent to solving the system of PDEs,


Integrate both sides of the first PDF with respect to
:

where
is some function independent of
. Then differentiatng with respect to
, we have


and so
is indeed conservative, with

I am pretty sure that the answer is 4/5, hope this helped :)
Answer:
The first table
Step-by-step explanation:
You have to make sure that x is unique throughout.
First Table: the inputs are 2, 4, 6, 7
each input value is different or unique
Second Table: input values are 3, 5, 3, 5
three and five repeat themselves, so there is not a function
Third Table: input values are -2, 0, 1, -2
negative 2 repeats itself so it is not unique