Order of Partial Differentiation

$$\frac{\partial \frac{\partial f(x,y)}{\partial x} }{\partial ... ...\frac{\partial\frac{\partial f(x,y)}{\partial y} }{\partial x}$$

For example if p=p(V,T) = nRT/V, then

$$\frac{\partial p}{\partial T} = nR/V \,\,;\,\, \frac{\partial p}{\partial V} \ =-nRT/V^2$$

so

$$\frac{\partial \frac{\partial p}{\partial T}}{\partial V} = -... ...{\partial \frac{\partial p}{\partial V}}{\partial T} = -nR/V^2$$

i.e., reversing the order of partial differentiation is permissible.