The D(f) command applies the differential operator to an expression.  The command extends the differential operator D to operate on Vectors and Vector valued procedures.

$\mathrm{with}\left(\mathrm{VectorCalculus}\right)\:$

$\mathrm{D}\left(\sin \right)$

$\cos$

$\mathrm{D}\left(⟨x^2\,y^2\,z^2⟩\right)$

$\mathrm{D}\left[2,1\right]\left(\left(x\,y\right)\mapsto ⟨y\cdot x^2+y^2+3\cdot y\cdot x\,x^2\cdot y^3\,y\cdot x⟩\right)\left(x\,y\right)$