Figure shows two dipole moments parallel to each other and placed at a distance $x$ apart (where $x$ is very large compared to size of dipoles) then

The electric field at the location of $P_2$from$P_1,E_1=\frac{k{P}_1}{x^3}$  Now, force on $P_2$ due to electric field ${\mathrm{E}}_1,F=P_2·\frac{dE}{dx}$

$$\begin{gathered} =P_2\frac{d}{dx}\left(\frac{k{P}_1}{x^3}\right) \\ =P_2\left(-\frac{3k{P}_1}{x^4}\right) \\ =-\frac{3k{P}_1{P}_2}{x^4} \end{gathered}$$

Here negative sign indicates that force is attraction.