This is a very short section and is here simply to
acknowledge that just like we had differentials
for functions of one variable we also have them for functions of more than one
variable. Also, as we’ve already seen in
previous sections, when we move up to more than one variable things work pretty
much the same, but there are some small differences.
Given the function the differential dz or df is given by,
There is a natural extension to functions of three or more
variables. For instance, given the
function the differential is given by,
Let’s do a couple of quick examples.
Example 1 Compute
the differentials for each of the following functions.
(a)
(b)
Solution
(a)
There really isn’t a whole lot to these outside of some
quick differentiation. Here is the
differential for the function.
(b)
Here is the differential for this function.

Note that sometimes these differentials are called the total differentials.