Apply Eq. 7.7 directly to Eqs. 7.1 and 7.2 and derive the relations of Eqs. 7.15 and

Question:

Apply Eq. 7.7 directly to Eqs. 7.1 and 7.2 and derive the relations of Eqs. 7.15 and 7.16.
Eq. 7.1
du = Tds - Pdv
Eq. 7.2
dh = Tds + vdP
Eq. 7.7
dz = (∂z/∂x)y dx + (∂z/∂y)x dy
Eq. 7.15
(∂u/∂s)v = T and (∂u/∂v)x = - P
Eq. 7.16
(∂g/∂P)T = v and (∂g/∂T)P = - s