If an effect allows you to cast Dyadrine without paying its mana cost, X will be 0.

If an effect requires you to pay some amount of mana to prevent Dyadrine from being countered, as Divert Disaster does, that mana wasn’t spent to cast Dyadrine and will not be taken into account for Dyadrine’s second ability.

If a copy of Dyadrine is created on the stack, no mana was spent to cast the copy. The amount of mana spent to cast the original spell is not copied.

Dyadrine’s second ability cares about the amount of mana that was actually paid to cast Dyadrine. Any effects that increase or decrease the cost to cast it (including the “commander tax” in a Commander game) will also be taken into account.