If x = f(u,v,...) then
The first set of terms represent the contributions from the deviations of individual variables and the second set of terms represents the covariance of pairs of variables. This is defined as:
. Fortunately this term is
usually zero if the variables u and v are uncorrelated.
Some examples:
If x = au + bv then 
.
If x = auv then 
.
If 
then 
.
We also find that the error in a weighted mean is 
.