ex11.rb

# derivative_scheme.(f).(x) shall be a function of epsilon
derivative_sheme = -> f {
  -> x {
    -> eps {
      div.( minus.(plus_eps.(eps).(f), min_eps.(eps).(f) ), mult.(const.(2), const.(eps))).(x)
    }
  }
} 

# And the derivative operator:
# Let's fix the treshold at tres = 1e-16
derivate = -> f {
  -> x {
    lim.(derivative_sheme.(f).(x),1,1e-16).(0) # limit of the derivative scheme of f(x), taken at epsilon = 0
  }
}

# Isn't that fancy ? We juste define the derivative operator 
# exactly as being the limit of (f(x + e) - f(x - e))/(2e) when epsilon -> 0