  In the present paper, we consider the Cauchy problem of fourth order
nonlinear Schr\"odinger type equations with a derivative nonlinearity. In one
dimensional case, we prove that the fourth order nonlinear Schr\"odinger
equation with the derivative quartic nonlinearity $\partial _x
(\overline{u}^4)$ is the small data global in time well-posed and scattering to
a free solution. Furthermore, we show that the same result holds for the $d \ge
2$ and derivative polynomial type nonlinearity, for example $|\nabla | (u^m)$
with $(m-1)d \ge 4$.
