show that for the function f(x)=2xln*x-1, the newton-raphson formula can be expressed as

X(n+1)= (X(n)+1/2)/(1+ln*X(n)) , The (n) and (n+1) terms are subscript.

I have tried using the product rule for f(x) and then some algebraic jiggery but cant even get close to the raphson result.I think I may have made an error in the algebra somewhere.

Can anyone please give any suggestions???

Thank you.