These functions were first studied in
HELM booklet
18. As a reminder:
-
a function of the two independent variables
and
may be written as
-
the first and second order partial derivatives are
,
,
,
and
.
Consider, for example, the function
. The first and second partial derivatives are
The number of independent variables is not restricted to two. For example, if
is a function of the three variables
,
and
, say
then:
Similarly, if
is a function of the four variables
,
,
and
say
then
, etc.