ThreeDivergence[exp, CV[p, i]] calculates the partial derivative of exp w.r.t. p^i.
ThreeDivergence[exp, CV[p, i], CV[p,i], ...] gives the multiple derivative.
Owing to the fact that in FeynCalc dummy Cartesian index are always understood to be upper indices, applying ThreeDivergence to an expression is equivalent to the action of \nabla^i = \frac{\partial}{\partial p^i}.
CSP[p, q]
ThreeDivergence[%, CV[q, i]]\overline{p}\cdot \overline{q}
\overline{p}^i
CSP[p - k, q]
ThreeDivergence[%, CV[k, i]](\overline{p}-\overline{k})\cdot \overline{q}
-\overline{q}^i
CFAD[{p, m^2}, p - q]
ThreeDivergence[%, CVD[p, i]]\frac{1}{(p^2+m^2-i \eta ).((p-q)^2-i \eta )}
\frac{2 q^i-2 p^i}{(p^2+m^2-i \eta ).((p-q)^2-i \eta )^2}-\frac{2 p^i}{(p^2+m^2-i \eta )^2.((p-q)^2-i \eta )}
Differentiation of 3-vectors living in different dimensions (3, D-1, D-4) works only in the t’Hooft-Veltman scheme
ThreeDivergence[CVD[p, i], CV[p, j]]
\text{\$Aborted}
FCSetDiracGammaScheme["BMHV"];ThreeDivergence[CVD[p, i], CV[p, j]]\bar{\delta }^{ij}