For each of the following, prove that f and g are differentiable on their domains, and find

Question:

For each of the following, prove that f and g are differentiable on their domains, and find formulas for D(f + g)(x) and D(f • g)(x).
a) f(x, y) = x - y, g(x, y) = x2 + y2
b) f(x, y) = xy, g(x, y) = x sin x - cos y
c) f(x, y) = (cos(xy), x log y), g(x, y) = (y, x)
d) f'(x, y, z) = (y, x -z), g(x, y, z) = (xyz, y2)