c$)$ Given that a fluid flows through a duct which resulted into its

changes in momentum and pressure. The magnitude of such changes

is represented as:

$(\frac{\text{d}\text{e}\text{l}\text{U}}{\text{d}\text{e}\text{l}\text{V}}{)}_T=T(\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{T}}{)}_V-P$

Hence or otherwise, show that:

$\frac{1}{T}\frac{de{l}^{2}U}{\text{d}\text{e}\text{l}\text{T}\text{d}\text{e}\text{l}\text{V}}=\frac{1}{T}[(\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{T}}{)}_V+\frac{de{l}^{2}U}{\text{d}\text{e}\text{l}\text{V}\text{d}\text{e}\text{l}\text{T}}]-\frac{1}{T^2}[P+(\frac{\text{d}\text{e}\text{l}\text{U}}{\text{d}\text{e}\text{l}\text{V}}{)}_T]$

marks$)$