It is more complicated (or easy) as this, so I'll give a very basic universal rule.

All skills that use Magicka scale off spell damage
All skills that use Stamina scale off weapon damage

So for example:
Venom Arrow, uses stamina, so it is effected by weapondamage.
Impulse (destruction staff skill) uses magicka and so it is effected by spell damage (even though a staff is a weapon)
Inner fire (undaunted skill) uses magicka, so it is effected by spell damage
However, if you morph inner fire to inner beast it suddenly uses stamina and so it is effected by weapondamage.