  In this article, we study the derivations of group algebras of some important
groups, namely, dihedral ($D_{2n}$), Dicyclic ($T_{4n}$) and Semi-dihedral
($SD_{8n}$). First, we explicitly classify all inner derivations of a group
algebra $\mathbb{F}G$ of a finite group $G$ over an arbitrary field
$\mathbb{F}$. Then we classify all $\mathbb{F}$-derivations of the group
algebras $\mathbb{F}D_{2n}$, $\mathbb{F}T_{4n}$ and $\mathbb{F}(SD_{8n})$ when
$\mathbb{F}$ is a field of characteristic $0$ or an odd rational prime $p$ by
giving the dimension and an explicit basis of these derivation algebras. We
explicitly describe all inner derivations of these group algebras over an
arbitrary field. Finally, we classify all derivations of the above group
algebras when $\mathbb{F}$ is an algebraic extension of a prime field.
