  The n-fold Darboux transformation (DT) is a 2\times2 matrix for the
Kaup-Newell (KN) system. In this paper,each element of this matrix is expressed
by a ratio of $(n+1)\times (n+1)$ determinant and $n\times n$ determinant of
eigenfunctions. Using these formulae, the expressions of the $q^{[n]}$ and
$r^{[n]}$ in KN system are generated by n-fold DT. Further, under the reduction
condition, the rogue wave,rational traveling solution, dark soliton, bright
soliton, breather solution, periodic solution of the derivative nonlinear
Schr\"odinger(DNLS) equation are given explicitly by different seed solutions.
In particular, the rogue wave and rational traveling solution are two kinds of
new solutions. The complete classification of these solutions generated by
one-fold DT is given in the table on page.
