  We investigate the boson-fermion duality relation for the case of quantum
integrable derivative $\delta$-function bose gas. In particular, we find out a
dual fermionic system with nonvanishing zero-range interaction for the simplest
case of two bosonic particles with derivative $\delta$-function interaction.
The coupling constant of this dual fermionic system becomes inversely
proportional to the product of the coupling constant of its bosonic counterpart
and the centre-of-mass momentum of the corresponding eigenfunction.
