Lifting derivations and $n-$weak amenability of the second dual of a Banach algebra

We show that for $n\ge 2$ the $n-$weak amenability of the second dual ${\text{A}}^{\ast \ast }$ of a Banach algebra $\text{A}$ implies that of $\text{A}$. We also provide a positive answer for the case $n=1,$ which sharpens some older results. Our method of proof also provides a unified approach to give short proofs for some known results in the case where $n=1$.