Fix n, k E N+ with n > k. Let F : R* -> Rock and define G : Rk x R"-k -> R"-k by G(x, y) = y -F(x) for (x, y) ERk x R"-k. Fix a E Rk and p = (a, F(a)) ERk x R"-k. Assume Fis C. Define S = {(x, y) ERk x R"-k : y = F(x)} so S is both the graph of F and a level set of G. Prove that TDS = ker(dGp)