How can I deduce the generalized form of Newton Raphson method?

Question

I know the formula but can't derive it from the Newton-Raphson's method of finding roots of f(x)=0.

the formula that I know is x1 = x0 - k * f(x0) / f`(x0)
where k = number of times a single root is repeating for f(x) = 0.

plz help!!

no, that is okay to derive Newton Raphson method from taylor's theorem.
but I want to derive the GENERALIZED form of newton raphson method.

Answer 1

You can derive Newton Raphson method by approximation of higher mean value theorem or from taylor series.