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An exact expression in terms of density matrices (DMs) is derived for hF [n]/hn(r), the functional derivative of the Hohenberg-Kohn functional. The derivation starts from the differential form of the virial theorem, obtained here for an electron system with arbitrary interactions, and leads to an expression taking the form of an integral over a path that can be chosen arbitrarily. After applying this approach to the equivalent system of noninteracting electrons (Slater-Kohu-Sham scheme) and combining the corresponding result with the previous one, an exact expression for the exchangecorrelation potential v",(r) is obtained which is analogous in character to that for 6F[n]/bn(r), but involving, besides the interacting-system DMs, also the noninteracting DMs. Equating the former DMs to the latter ones, we reduce the result for the exact v",(r) to that for an approximate exchange-only potential v"(r). This leads naturally to the Harbola-Sahni exchange-only potential. PACS number(s): 31.15.Ew, 71.10.+x, 31.25.v, 71.45.Gm

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