Fundamental Thermodynamics Relation

[Silviu]

Hello! I am a bit confused by the formula $dU = TdS - PdV$. If I want to compute for example $\frac{\partial U}{\partial V}$ I obtain $-P$, but how should I proceed to obtain, for example $\frac{\partial U}{\partial P}$ or $\frac{\partial P}{\partial T}$ which are not obvious from the equation? Thank you!

 

[Chestermiller]

For those partial derivatives you mention, you need to specify what is being held constant.