  The aim of this paper is to propose a theory of derivations for quandles.
Given a quandle $A$ admitting an action by a quandle $Q$, derivations from $Q$
to $A$ are introduced as twisted analogues of quandle homomorphisms. It is
shown that for each quandle $Q$ there exists a unique $Q$-quandle
$\mathcal{A}_Q$ (the derived quandle of $Q$) such that derivations from $Q$ to
any $Q$-quandle $A$ are in bijective correspondence with $Q$-quandle
homomorphisms from $\mathcal{A}_Q$ to $A$. Further, it is proved that the set
of all derivations to an abelian $Q$-quandle $A$ has the structure of an
abelian quandle, and inherits many other properties from $A$. In the end, the
ideas are extended to the setting of virtual quandles.
