fsolve or nSolve with the option newton_solver

newton_solver is the standard Newton method. The algorithm starts at an init value x₀, then we search the intersection x₁ of the tangent at x₀ to the graph of f, with the x axis, the next iteration is done with x₁ instead of x₀. The x_i sequence is defined by

x₀ = x₀,    x_n+1 = x_n - $${\frac{{f(x_n)}}{{f'(x_n)}}}$$

If the Newton method converges, it is a quadratic convergence for roots of multiplicity 1.
Input :

fsolve((cos(x))=x,x,0,newton_solver)

Output :

0.739085133215