n-Weak Amenability of T-Lau Product of Banach Algebras

Given a morphism $T$ from a Banach algebra $B$ into a commutative Banach algebra $A,$ we explain explicitly the derivations from $T$-Lau product $A \times_T B$ into its $n^{th}$-dual $(A \times_T B)^{(n)}$ from which we obtain general necessary and sufficient conditions for $A \times_T B$ to be $n$-weakly amenable.