University Maths Notes: Calculus – The Total Derivative
If f is a function of several variables, the total derivative
enables us to find the change in f as the function moves a small
distance between two points
and
We find all the partial derivatives
then
the total derivative
(1)
and this is roughly equal to
with
the degree of accuracy increasing as
and
get
closer together.
We evaluate (1) at
Example: If
find
and
estimate the change in
asmoves
along a curve between
and
With
and