Suppose U1 and U2 are two open sets in R^n with U1∩U2 non-empty and path connected. Suppose there exists an f1 : U1 → R and f2 : U2 → R, both twice continuously differentiable such that d f1 = d f2 on U1 ∩ U2. Then there exists a twice differentiable function F : U1 ∪U2 → R such that dF = d f1 on U1 and dF = d f2 on U2