The problem is attached in the picture.
The Attempt at a Solution
I'm aware that:
dU = T dS - P dV
∫ dU = ∫ (T) dS - ∫ P dV
Are they assuming that T, P are constant so
U = TS - PV
∂U/∂X = T (∂S/∂X) - P (∂V/∂X)
Or is there a way to directly change dU to ∂U?