Proving Normality of [G,G] in G: A Commutator Question

[MathematicalPhysicist]

Perhaps someone will help me in this.
I need to prove that the group [G,G] of elements of the form $$gh g^{-1}h^{-1}$$ where g,h in G, is normal in G, i.e if k is in G, then $$kghg^{-1}h^{-1}k^{-1}=aba^{-1}b^{-1}$$ for some a,b in G.
I tried writing it as $$kghkk^{-1}g^{-1}h^{-1}k^{-1}$$, but here is where my attmempt run down the mill, as in not successful.
Any hints?

 

[yyat]

Conjugate two elements g,h by the same element and compute the commutator.

 

[MathematicalPhysicist]

Ok, thanks.