In this paper, we aim to consider the k = (k 1 , k 2 , · · · , k d)-th order derivatives β (k) (T, x) of self-intersection local time β(T, x) for the linear fractional stable process X α,H in R d with indices α ∈ (0, 2) and H = (H 1 , · · · , H d) ∈ (0, 1) d. We first give sufficient condition for the existence and joint H ¨ older continuity of the derivatives β (k) (T, x) using the local nondeterminism of linear fractional stable processes. As a related problem, we also study the power variation of β (k) (T, x).