The diff(f, v) calling sequence is an extension of the top-level diff that performs coordinate-wise differentiation on Vectors (including vector fields), in the coordinate systems of the Student[VectorCalculus] package.  If f is not a Vector, the arguments are passed to the top-level diff command.

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

$\mathrm{diff}\left(⟨t\,t^2\,t^3⟩\,t\right)$

$\mathrm{diff}\left(⟨\cos \left(st\right)\,\sin \left(st\right)⟩\,s\,t\right)$

$\mathrm{SetCoordinates}\left(\mathrm{spherical}\left[r,\mathrm{\phi },\mathrm{\theta }\right]\right)$

${\mathrm{spherical}}_{r,\mathrm{\phi },\mathrm{\theta }}$

$F≔\mathrm{VectorField}\left(⟨ar\,0\,0⟩\right)$

$\mathrm{diff}\left(F\,\mathrm{\phi }\right)$

$\mathrm{diff}\left(F\,a\right)$