This article deals with the algebra of gH-differentiable interval-valued functions. Specifically, we give conditions for the gH-differentiability of the sum and the gH-difference of two gH-differentiable interval-valued functions; we also consider the product and the composition of a differentiable real function and a gH-differentiable interval-valued function. We briefly review existing results on the topic and show that some of them are not correct. New properties are also presented. Therefore, this article corrects, complements and generalizes previously obtained results. Some examples and counterexamples illustrate the theory.