In this article algorithmic differentiation is applied to compute the sensitivities of the price of an American option, which is computed by the Longstaff-Schwartz algorithm. Adjoint algorithmic differentiation methods speed up the calculation and make the results more accurate and robust compared to a finite difference approximation. However, adjoint computations require more memory due to the storing of intermediate results. One possibility to reduce these memory requirements is to use a technique called checkpointing: Instead of storing all intermediate results the required values are recomputed. Another possibility is to apply a pathwise adjoint approach, which results from an analysis of the Longstaff-Schwartz algorithm and the exploitation of its features. The presented approach is embarrassing parallel and yields the same results as the other adjoint methods, but it reduces the computational effort as well as the memory requirements of the computation to the level of a single pricing calculation.