Please answer both (a) and (b).

5. (40 pts) Material derivative (a) Consider an observer who measures the density p(1,t) of a flow system at a fixed point x every At time periods, e.g. at times t, t + At, t +2At, etc. Show that the observer measurements determine the time derivative Op/at (b) Consider now an observer who moves with the system velocity u and measures the density p(x, t) every At time periods, e.g. the observer measures the density p at (x, t), then at (x + Art + At), etc. Show that the observer measurements determine the material derivative Dp/Dt