In the paper [l], H.T.Banks and M.Q.Jacobs have discussed the one order differential of the multifuntions ?:R^m→A(Rⁿ)，Their result has been improved in this paper and the sufficient and necessary conditions for the differentiability are given respectively. The limitation of (3.2) in [l] is proved to be unnecessary and the sufficient and necessary conditions for the differentialbility of ? are found. Furthermore，the sufficient and necessary conditions for the higher order differentialbility of ? are gained and a calculus formula is given.