In my case, you can approximate the denominator term,
f'(x)
with a forward, backward, or central difference.
So, just to elaborate, if you have,
f(x) = x^2
and,
f(x+h) = (x+h)^2
f(x-h) = (x-h)^2
for some small h (gridspace)
Then, using Central Difference your Newton-Raphson...