The Vector Derivative $\vec{\nabla}$

The derivative operator $\vec{\nabla}={\partial\ \over\partial x_i}\hat{e}_i$ transforms like a vector. We may take the gradient of a function $\vec{\nabla}f={\partial f\over\partial x_i}\hat{e}_i$, the divergence of a vector field $\vec{\nabla}\cdot \vec{B}={\partial\ \over\partial x_i}B_i$, or the curl of a vector field $\vec{\nabla}\times \vec{B}={\partial\ \over\partial x_i}B_j\epsilon_{ijk}\hat{e}_k$.