= Divergence of a Cartesian second-rank tensor
{title2=$U_i=\partial_jT_{ij}$}
For a constant orthogonal Cartesian coordinate change $x'=Rx$, a <Cartesian second-rank tensor> obeys $T'_{ij}=R_{ik}R_{jl}T_{kl}$. The <chain rule> gives $\partial'_j=R_{jm}\partial_m$. Consequently $\partial'_jT'_{ij}=R_{ik}R_{jl}R_{jm}\partial_mT_{kl}=R_{ik}\partial_lT_{kl}$, the transformation rule for a <vector>. Under non-Cartesian position-dependent coordinate changes, partial derivatives must be replaced by the appropriate <covariant derivative>.
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