How newton rephson method is better than bisection method?

The Newton-Raphson method is generally more efficient than the bisection method because it has a quadratic convergence rate, meaning it can achieve much higher accuracy with fewer iterations, especially when the initial guess is close to the root. In contrast, the bisection method has a linear convergence rate and requires the function to change signs over an interval, which can lead to slower convergence. However, the Newton-Raphson method requires the calculation of the derivative and may not converge if the initial guess is far from the root or if the function is not well-behaved, making it less reliable in some cases. Overall, when applicable, Newton-Raphson tends to be faster and more efficient than the bisection method.