Examine whether S^-(2r/o^2) could be the price of a traded derivative security. Need to use the black scholes merton differential equation. I do not understand how the partial derivatives of the model are substituting. For example when f = S^-(2r/o^2) the term on the bsm differential equation af/at = 0; af/as = (-2r/o^2) x S^[-(2r/o^2)-1]; finally the term of the equation a^2f/aS^2 = (2r/o^2) x [(2r/o^2)+1] x S^[-(2r/o^2)-2]. How all these terms are found? The one for the partial derivatives?