thermodynamics - Determine the Dependence of $S$ (Entropy) on $V$ and $T$

Why can the equation $$dS= \frac{1}{T} dU + \frac{P}{T} dV$$ be expressed as $$dS= \left. \frac{\partial S}{\partial T} \right|_V dT + \left. \frac{\partial S}{\partial V} \right|_T dV \quad?$$