Yes.

Ordinarily when we do differentials everything is signed so that if then

(*)

and the and are either positive or negative (respectively.)

However, when we do error analysis things are different because we always take our error to be positive, say — therefore the corresponding change in , lies between plus and minus this:

.

we attribute a potential error in our measurements of and — say (and ). These errors can be positive *or* negative. Hence, suppose that is negative and is positive; and suppose further that the *actual* errors (we only know that we are correct to within a specified range, but in theory there is a measured value and an actual value) and are negative and positive, and moreover, at their maxima. Using the definition of a differential (how we estimate the change in due to changes in and ), our estimation of the error:

,

that is we don’t necessarily have cancellations so we have to take absolute values.

For estimating changes in the dependent variable due to changes in the independent variables we use (*). For error analysis we use the following:

where , and .

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