Problem 1: Let (f(u, v) = (tan(u) + eᵛ, u² - v²)) and (g(x, y) = (eˣy, xy)).
(a) Calculate (D(f ∘ g)(1, 1)) using the chain rule, i.e., without computing (f ∘ g) directly.
(b) Let (vecc(t) = (eᵗ + t², cos(t) - 2t)). Find the unit tangent vector to the curve ((f ∘ g ∘ vecc)(t)) when (t = 0).