I'm playing around with apply-partially and I'm confused about what gets returned when calling this function. The documentation states that apply-partially returns a function, but then I'd expect to be able to do the following:

(defun add-numbers (a b)
  (+ a b))
(defun add2 (apply-partially 'add-numbers 2))

and then call the function:

(add2 3)

OR:

(funcall add2 3)

Unfortunately this throws an error. When I do everything inside of a let, however, it does work and I get "5" back:

(let ((add2 (apply-partially 'add-numbers 2)))
  (funcall add2 3))

I thought maybe the difference was that let doesn't use defun, as I do above, but then I would expect the following to work:

(defvar add2 (apply-partially 'add-numbers 2))
(funcall
 add2 3)

but that doesn't work either. So what am I missing? Is it not possible to assign the return value of apply-partially outside of a let?