In[]:=
Manipulate​​symTable={U,H,F,G,S,V,p,T};RowFractionBox["∂"symTable[[X]],"∂"symTable[[Y]]]//DisplayForm,
""
symTable[[Z]]
," = ",​​IfToString@symTable[[Y]]ToString@symTable[[Z]],"indefinite",Det@Outer[tpl@@Flatten[{#1,#2}]&,{symTable[[X]],symTable[[Z]]},{{p,T},{T,p}},1]Det@Outer[tpl@@Flatten[{#1,#2}]&,{symTable[[Y]],symTable[[Z]]},{{p,T},{T,p}},1]//.​​tpl[U,b_,c_]Ttpl[S,b,c]-ptpl[V,b,c],​​tpl[H,b_,c_]Ttpl[S,b,c]+Vtpl[p,b,c],​​tpl[F,b_,c_]-Stpl[T,b,c]-ptpl[V,b,c],​​tpl[G,b_,c_]-Stpl[T,b,c]+Vtpl[p,b,c],​​tpl[V,p,T]-
κ
T
V,​​tpl[V,T,p]αV,​​tpl[S,p,T]-αV,​​tpl[S,T,p]
C
p
T
,​​tpl[T,_,T]0,​​tpl[p,_,p]0,​​tpl[T,T,p]1,​​tpl[p,p,T]1​​​​​​//Simplify,Style["Partial derivatives to measurables",Bold,FontSize15],​​Style[" ",Bold,FontSize14],​​StyleRow
"∂X"
"∂Y"
,
""
"Z"
," = ",FontSize14,​​Style[" ",Bold,FontSize14],​​Style[" U H F G S V p T",FontSize13],​​{{X,5},1,8,1,Appearance"Labeled"},{{Y,8},1,8,1,Appearance"Labeled",TicksTrue},{{Z,6},1,8,1,Appearance"Labeled"},SaveDefinitionsTrue
Out[]=
​
Partial derivatives to measurables
∂X
∂Y

Z
=
U H F G S V p T
X
5
Y
8
Z
6
∂S
∂T

V
=
C
p
T
-
V
2
α
κ
T