and you’ve used:

(put 'deriv '+ deriv-sum)


But ‘+ is the operator and ‘deriv is the type.
In your implementation there is clearly no problem as you make the hash table’s key a tuple of both and there is only 1 implementation type - ‘deriv..
The definitions of put and get are not clear that actually the type parameter of both are lists of types.
Only the code in the book makes this explicit though e.g.

(put 'real-part '(rectangular) real-part)
(put 'imag-part '(rectangular) imag-part)


especially within the implementation of apply-generic

(define (apply-generic op . args)
(let ((type-tags (map type-tag args)))
(let ((proc (get op type-tags)))
(if proc
(apply proc (map contents args))
...
...


It’s a little confusing but it seems get scans the list of types for the first match and only returns false if no match is found against the list.