Differentials
In this section we’re going to introduce a notation that we’ll be seeing quite a bit in
the next chapter. We will also look at an application of this new notation.
Given a function
we call
dy
and
dx
differentials and the
relationship between them is given by,
Note that if we are just given
then the differentials are
df
and
dx
and
we compute them in the same manner.
Let’s compute a couple of differentials.
Example 1
Compute the differential for each of the following.
(a)
(b)
(c)
Solution
Before working any of these we should first discuss just what we’re being asked to find here. We
defined two differentials earlier and here we’re being asked to compute a differential.
So, which differential are we being asked to compute? In this kind of problem we’re being asked
to compute the differential of the function. In other words,
dy
for the first problem,
dw
for the
second problem and
df
for the third problem.
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 Fall '08
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