Although this definition is perhaps not as explicit as the above, if such an operator exists, then it is unique, and in the one-dimensional case coincides with the original definition. (In this case the derivative is represented by a 1-by-1 matrix consisting of the sole entry "f"'("x").) Note that, in general, we concern ourselves mostly with functions being differentiable in some open neighbourhood of formula_9 rather than at individual points, as not doing so tends to lead to many pathological counterexamples.