Hey I'm having a little problem with this question

I can do the first one absolutely fine, just take the total derivative of H and substitute in the expression in for dU then use the fact that mixed partials commute.The enthalpy of a gas is defined by where U satisfies Determine a relationship between the differentials of H, S and p. Hence show that

By regarding U as a function of p and V show that

The second part I'm having more trouble with, any chance of a hint?

Cheers