The divergence of the vector field \[ \mathbf{F}(x,y,z)=x^{2}yz^{2}\mathbf{i}+(2xz+y^{3})\mathbf{j}+x^{2}y^{3}z \mathbf{k} \]
is \[ {\rm div}\mathbf{F}=\dfrac{\partial }{\partial x}(x^{2}yz^{2})+\dfrac{ \partial }{\partial y}(2xz+y^{3})+\dfrac{\partial }{\partial z} (x^{2}y^{3}z)=2xyz^{2}+3y^{2}+x^{2}y^{3} \]