Question

Two functions. f(x, y) and g(x, y) are said to be functionally dependent, if one is a function of the other, that is, if there exists a single-variable function k(t) such that f(x, y) = k[g(x, y)] for all x and y. Show that in this case, ∂(f, g)/∂(x, y) vanishes identically. Assume that all necessary conditions exist

Answer 1

cause the 2 functions are dependent and one can be expressed in terms of another, then we can prove that the jacobian matrix should be 0 and g f can not solve for x y.
btw, I dont like the word "cheating", cause math is a subject that needs discussing, sometimes we have to discuss with others to get inspired. anyway, good luck with ur advanced calc!