Set of functions whose

I am confused while writing a mathematical definition. Do we say

• A set of functions whose derivative is equal to 1, or
• A set of functions whose derivatives are equal to 1?

I would prefer the first option but it feels grammatically incorrect.

The first one would imply the derivative of the set, or at best it will be ambiguous, if functions somehow share the same derivative.

The second - derivatives of the functions. Correct.

And "the" instead of "a" is more appropriate.

I have always used the first one despite the occasional qualm. The principle is that "whose" refers to the collection and so does not get the plural. We do not often use the word "derivatives" everyday but we do in mathematics often. I think that is where we get the rub.