### Derived subgroup proofs

Let G' be the derived subgroup. Prove: a) If G' is a subgroup of H and H is a subgroup of G, show that H is normal in G; b) If K is a normal subgroup of G, then K' is a normal subgroup of G c) Suppose f:G --> H is an epimorphism, with ker(f)=K, then H is abelian iff G' is a subgroup of K. I need a detailed proof of t