There is a technical point in the proof above which is worth noting: applying the Chain Rule to formula_110 requires that formula_116 already be Differentiable. This is where we use our assumptions about formula_93. As mentioned above, the partial derivatives of formula_116 are given by the formulas formula_114 and formula_119. Since formula_131 is continuous, its integral is also a continuous function, and since formula_93 is also continuous, these two results show that both the partial derivatives of formula_116 are continuous. Since continuity of partial derivatives implies differentiability of the function, formula_116 is indeed differentiable.