In a recent publication Chen & Zadrozny (2001) derive some equations for efficiently computing eA and ∇ eA, its derivative. They employ an expression due to Bellman (1960), Snider (1964) and Wilcox (1967) for the differential deA and a method due to Van Loan (1978) to find the derivative ∇eA. The present note gives a) a short derivation of ∇ eA by way of the Bellman-Snider-Wilcox result, b) a shorter derivation without using it. In both approaches there is no need for Van Loan’s method.