I have the list of experimental values: $$\{w_i \pm \Delta w_i\},$$ where $w_j$ is a mean value and $\Delta w_i$ is an error.
I want to calculate the second list $\{a_i \pm \Delta a_i\}$ according to the rule $$a_i = \frac{w_i / A_i}{\sum_j w_j / A_j},$$ where $A_i$ is some constant for $i$.
How to define errors $\Delta a_i$? Is it the right way?
$$\Delta a_i = \frac{1}{A_i} \frac{\Delta w_i |\sum_j w_j/A_j| + |w_i|\sum_j \Delta w_j/A_j}{(\sum_j w_j/A_j)^2}$$