  In this letter,the designable integrability(DI) of the variable coefficient
derivative nonlinear Schr\"odinger equation (VCDNLSE) is shown by construction
of an explicit transformation which maps VCDNLSE to the usual derivative
nonlinear Schr\"odinger equation(DNLSE). One novel feature of VCDNLSE with DI
is that its coefficients can be designed artificially and analytically by using
transformation. What is more, from the rogue wave and rational traveling
solution of the DNLSE, we get two kinds of rogue waves of the VCDNLSE by this
transformation. One kind of rogue wave has vanishing boundary condition, and
the other non-vanishing boundary condition. The DI of the VCDNLSE also provides
a possible way to control the profile of the rogue wave in physical
experiments.
