  When dealing with certain mathematical problems, it is sometimes necessary to
show that some function induces a metric on a certain space. When this function
is not a well renowned example of a distance, one has to develop very
particular arguments that appeal to the concrete expression of the function in
order to do so. The main purpose of this paper is to provide several sufficient
results ensuring that a function of two variables induces a distance on the
real line, as well as some necessary conditions, together with several examples
that show the applicability of these results. In particular, we show how a
hypothesis about the sign of the cross partial derivative of the candidate to
distance is helpful for deriving such kind of results.
