In this article, we propose to establish the proof of the differentiability of the solution of a system of nonlinear equations disrupted following a certain number of parameters. Two main results have been derived. In the first theorem, differentiability is defined according to FFrechet.The proof is given using the theorem of reciprocal functions in Banach spaces with prior evidence of Frechet’s strict differentiability of adirect application. In the second theorem, differentiability is in a weaker form as to Frechet. Its proof requires the use of the Hadamard theorem of small disturbances of isomorphism in Banach spaces and the theorem of strict differentiability of inverse functions established in[10] (with a possible lack of differentiability in the sense of Fréchet).
