Nonlocal functional derivative of kinetic energy for the self-consistent Thomas-Fermi atom

It is well known in the Thomas-Fermi (TF) theory that the functional derivative $\delta T/\delta n\left(r\right),$ with $T$ the kinetic energy and $n\left(r\right)\mathrm{}$ the ground-state electron density, is proportional to $n^{2/3}\mathrm{}\left(r\right).$ But the differential equation satisfied by the TF self-consistent density for atoms is shown here to express $n^{1/3}\mathrm{}\left(r\right)\mathrm{}$ as a linear combination of ${\nabla }^{2}n/n$ and $(\nabla {n/n)}^2.$ Hence a nonlocal form for $\delta T/\delta n\left(r\right)\mathrm{}$ follows, solely in terms of these two variables.