Thermodynamics: Internal Pressure calculus

[thesidjway]

I'm extremely sorry for not using the template. One of my thermodynamics instructors used this relation to prove another result. I know what to do next and the other steps to end up at the final result but I don't know how this result came.
Is it simply mathematics that I'm not aware of, or is this a standard result? In both cases, kindly help me out! I'm stuck

[PLAIN]https://thesidjway.files.wordpress.com/2014/08/kaise.jpg[/IMG

Thanks in Advance
(I'm a first year undergraduate)

 

[Chestermiller]

The internal energy U was expressed as U = U (S,V). Have you had anything in your courses on partial differential equations yet? If not, you are going to have big trouble understanding this development as well as all the rest of thermodynamics. Sorry for the bad news.

Chet