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.

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

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

$\cos$

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

${\mathrm{D}}_{2\,1}\left(\left(x\,y\right)\→⟨y{x}^2\+y^2\+3xy\,x^2{y}^3\,xy⟩\right)\left(x\,y\right)$