thermodynamics - Why $dW=pdV$ is an inexact differential?

I remember an exact differential as:

$$A=M(x,y)dx+N(x,y)dy $$

and the condition for be exact is:

$$\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}. $$

Can I use that definition to proof that $dW=pdv$ is not an exact differential?

I was thinking in use $W=W(p,V)$ and calculate

$$dW=\frac{\partial W}{\partial p}dp+\frac{\partial W}{\partial V}dV$$

and try to find a way to refute the idea of an exact differential for $pdV$. Am I right?