Let $k$ be a field and $A$ a graded algebra (If it simplifies things, we can assume that $A$ is graded commutative, too). The Lie algebra of derivations is the linear subspace $Der(A)\subset End_k(A)$ of the vector space of $k$-endomorpisms of $A$, which is a solution set to the equation
$D(a\cdot b)= D(a)\cdot b +(-1)^{|a|} a \cdot D(b)$ for $a,b\in A$ and $D\in End_k(A)$.
The Lie bracket is given by the commutator $[D,D']:= D \circ D' - D' \circ D$
What is the right derived (dfg) Lie algebra of derivations, often written as $\mathbb{D}er(A)$, in this context?
Is it the dfg Lie algebra of graded derivations? I.e. $|D|\neq 0$ and we have
$D(a\cdot b)= D(a)\cdot b +(-1)^{|D|+|a|} a \cdot D(b)$