Recently,　Rao　investigated　the　estimations　for　the　derivative　of　a　density　in　GARCH-type　model　S=sigma　2Z　over　L2-risk　(Commun.　Stat.,　Theory　Methods　46:2396-2410,　2017).　This　paper　extends　those　estimations　to　Lp-risk　(1p＜).　In　addition,　we　provide　a　lower　bound　for　this　model,　which　indicates　one　of　our　convergence　rates　to　be　nearly-optimal.