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You can also use the Euclidean space.

E.<x,y> = EuclideanSpace()
cartesian = E.default_chart()
polar.<r,ph> = E.polar_coordinates()

Coframes

[(E2,(dx,dy)),(E2,(dr,dϕ)),(E2,(er,eϕ))].

Thus

dph = E.coframes()[1][2]
dph.display(polar)

dϕ=dϕ,

and

dph.display(cartesian)

dϕ=(yx2+y2)dx+(xx2+y2)dy.

Or

dph.apply_map(lambda h:h.subs({x^2+y^2:r^2}))
dph.display(cartesian)

dϕ=yr2dx+xr2dy.