  We study the greybody factor and Hawking radiation with a non-minimal
derivative coupling between the scalar field and the curvature in the
background of the slowly rotating Kerr-Newman black hole.
  Our results show that both the absorption probability and luminosity of
Hawking radiation of the scalar field increase with the coupling.
  Moreover, we also find that for the weak coupling $\eta<\eta_c$, the
absorption probability and luminosity of Hawking radiation decrease when the
black hole's Hawking temperature decreases; while for stronger coupling
$\eta>\eta_c$, the absorption probability and luminosity of Hawking radiation
increase on the contrary when the black hole's Hawking temperature decreases.
This feature is similar to the Hawking radiation in a $d$-dimensional static
spherically-symmetric black hole surrounded by quintessence \cite{chensong}.
