]> $$x_{N+1}=x_N-\frac{f\left(x\right)}{f\prime \left(x\right)}$$ $$x_{N+1}=x_N-\frac{2f\left(x\right)f\prime \left(x\right)}{2{\left(f\prime \left(x\right)\right)}^2-f\left(x\right)f″\left(x\right)}$$ $$x_{N+1}=x_N-\frac{f\left(x\right)}{f\prime \left(x\right)}-\frac{f″\left(x\right){\left(f\left(x\right)\right)}^2}{2{\left(f\prime \left(x\right)\right)}^3}$$