A remark on the domain of an unbounded derivation of a C1-algebra

It is shown that if A is an hermitian element of a C¹-algebra and A is in the domain of a closed unbounded derivation δ of the C¹-algebra and if ? is a continuously differentiable complex valued function defined on a closed interval containing the spectrum of A then $\text{?(A)}$ is in the domain of δ and the norm of $\text{δ(?(A))}$ is bounded by the norm of δ(A) times the least upper bound of the absolute value of the derivative of ?. This result is generalized to the case of continuously differentiable functions of several variables.