Answer
See explanation
Work Step by Step
Proof is simply obtained as, $$
\left(\frac{\partial s}{\partial v}\right)_u=\frac{-\left(\frac{\partial u}{\partial v}\right)_s}{\left(\frac{\partial u}{\partial s}\right)_v}\\=-\frac{-P}{T}=\frac{P}{T}
$$
