For each of the following functions, prove that f-1 exists and is differentiable in some nonempty, open

Question:

For each of the following functions, prove that f-1 exists and is differentiable in some nonempty, open set containing (a, b), and compute D(f-1){a, b)
a) f(u, v) = (3u - v, 2u + 5v) at any (a, b) ∈ R2
b) f(u, v) = (u + v, sin u + cos v) at (a, b) = (0, 1)
c) f(u, v) = (uv, u2 + v2) at (a, b) = (2, 5)
d) f(u, v) = (u3 - v2, sin u - log v) at (a, b) = (-1, 0)