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I have a function $z_{ik}$ dependent from $x_{ij}$ with this form:

$z_{ik}=(\sum_j x_{ij}\alpha_{jk}) \cdot ((\sum_jx^2_{ij})\beta_k)^{-1/2} $ for $i \in [1, N]$, $j \in [1, M]$ and $k \in [1, L]$

The $x_{ij}$ are measured with an error $\sigma_{ij}$, while $\alpha_{jk}$ and $\beta_k$ are assumed to be without error.

I have to compute the error on $z_{ik}$, i.e. $\sigma_{ik}$. I have computed $\frac{\partial z_{ik}}{\partial x_{ij}}$, but I'm wondering if I should introduce the covariance between $x_{in}$ and $z_{im}$, for $n, m \in [1, M]$.

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