need (e)(f)(g), thanks

6. With the notation used in this course and our book (a) What is N'(x)? (b) Show that SN'(d) = Ke-"(T-1)N'(d), where is the stock price at time t. In(S/K) + (r + 02/2)(T-t) di OVT-t In(S/K) + (r - 0/2)(T - t) d2 OVT-t (c) Calculate ad/as and ad2/as (d) Show that when c= SN(d) - Ke-r(T-1) (dz) that ac at 2VT where c is the price of a European call on a non-dividend-paying stock. (e) Show that dc/as = N(d) (f) Show that the c satisfies the Black-Scholes-Merton differential Equation. (g) Show that c =-rKe="{7-N(dz) SN'(di)vT - C c