I guess your equation is right?
then, just use the definition,
substitute and simplify
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.
Yes, using the formula x(n+1) = x(n) - f(x) /f'(x) is the way to go
f(x) = 2x(n) ln(x(n)) - 1
f'(x) = 2(ln(x(n)+1)
substitute these into the formula, multiply terms out & cancel those terms at the top that you can (should be the 2x(n) ln(x(n)) ones)
At least that's how I did it.