(define $N 3)
(define $params [| x y z |])
(define $g [| [| 1 0 0 |] [| 0 1 0 |] [| 0 0 1 |] |])

(define $d
  (lambda [%X]
    !((flip ∂/∂) params X)))

(d (f x y z))
;[| (f|1 x y z) (f|2 x y z) (f|3 x y z) |]

(df-normalize (d (d (f x y z))))
;[| [| 0 0 0 |] [| 0 0 0 |] [| 0 0 0 |] |]