Solutions:

1. H(2) = f(g(2)) = f(3.9) = 2.2;
2. H'(3) = f'(g(3))g'(3) = 0.4-512 = -0.17;
3. H(x) = f(g(x)) = 1.5 means g(x) = 2.2, x = 5.6;
4. H'(x) = f'(g(x))g'(x) = 0.2 means 0.4g'(x) = 0.2, x = 1.1.