Answer
$$\frac{\partial P}{\partial V}=-\frac{nRT}{V^2},$$
$$\frac{\partial P}{\partial T}= \frac{nR}{V}.$$
Work Step by Step
Since $ P=\frac{nRT}{V}=nRTV^{-1}$, then we have
$$\frac{\partial P}{\partial V}=-nRTV^{-2}=-\frac{nRT}{V^2},$$
$$\frac{\partial P}{\partial T}=nRV^{-1}= \frac{nR}{V}.$$
