In this article we show a characterization for a gH-differentiable interval-valued function through of properties of the (lateral) differentiability of its length function. Then, we give a procedure to classify a gH-differentiable interval-valued function according to their four types of gH-differentiability. Furthermore, using this classification, we propose a procedure to determine the points at which the sum of two gH-differentiable functions is gH-differentiable as well as to determine their type of gH-differentiability.