= Monomial uncertainty propagation
{title2=$\sigma_f^2/f^2\simeq\sum_{ij}a_ia_j\operatorname{Cov}(x_i,x_j)/(x_ix_j)$}
For positive measured inputs and $f=C\prod_i x_i^{a_i}$, <logarithmic differentiation> gives $df/f=\sum_i a_i\,dx_i/x_i$. Applying <propagation of uncertainty> yields the displayed <covariance> formula. For <independent> input errors it reduces to $\sigma_f/|f|\simeq[\sum_i(a_i\sigma_i/x_i)^2]^{1/2}$. If the input uncertainties are strict bounds rather than <standard deviations>, a first-order conservative bound is $|\Delta f|/|f|\lesssim\sum_i|a_i|\Delta x_i/|x_i|$. These are different statistical interpretations; a product formula alone does not choose between them.
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