Suppose I have a function $f(x_1, \dots, x_N)$, where $x_i$'s are random variables. $x_i$'s have SD $\sigma_i$, and are all independent.
There are two additional assumptions, that $f$ is approximately linear within the range $x^{'}_i \pm \sigma_i$; and secondly $x_i$ and $x_j$ are uncorrelated for $i \ne j$.
How to find the Var of $f$?