For a trader or an expert in finance, call him Mr Hyde, it is quite clear that a call or put spread is the derivative of an option and that a butterfly spread is the derivative of a call or put spread. Perhaps, he thinks, it should be approximately so. In fact, he knows that when a client asks for a digital option, he actually approximates that by taking large positions of opposite sign in European options with strikes as close as possible. So, for him a digital payoff is the limit of a call or put spread. He may also imagine what happens to the payoff of the butterfly spread as he increases the size of the positions and moves the strike prices closer and closer. He would get a tall spike with a tiny base, and, by iterating the process to infinity, he would get the Dirac delta function. So, gluing all the pieces together, Mr Hyde concludes that it is quite obvious that a Dirac delta function is the derivative of a digital payoff, which he knows is called the Heaviside unit step function.