why is it a derived quantity?
From wiki on SI Derived Unit:
The International System of Units (SI) specifies a set of seven base units from which all other units of measurement are formed, by products of the powers of base units. These other units are called SI derived units, for example, the SI derived unit of area is square metre (m2), and of density is kilograms per cubic metre (kg/m3). The number of derived units is unlimited.
Energy is derived since the joule's base units are kg⋅m2⋅s−2.
SI Base Units are:
metre for length (US English: meter)
kilogram for mass (note: not the gram)
second for time
ampere for electric current
kelvin for temperature
candela for luminous intensity
mole for the amount of substance.
Specifying and choosing base units is a minefield.
Do you ask your question this because you feel it is so important that it should be a base unit?
There's nothing sinister about the reason. All the quantities we use in Science are related and there's nothing particularly special about some, more than others. However,the base units are chosen mainly because they are relatively easy to measure and to specify reliably. Energy is a particularly hard thing to measure so it would not be an easy base unit to use. You would have to have a standard bucket of coal in Paris, a mass at the top of a high tower, somewhere to use as the standard or, a more modern version which involved the photons of a particular emission from a particular atom. Those examples may seem ridiculous but I can't think of a convenient alternative that a system of measurement could be based on.
Even mass is a difficult unit to specify and has relied on some arbitrary lumps of Platinum as standards. It is only recently that alternative ways of specifying the mass unit have been developed - involving counting atoms of a specific isotope of a specified element. ".wikipedia.org/wiki/Kilogram" [Broken]
By definition it's a derived unit because of what Drakkith wrote. Even something as simple as speed is a derived unit.
Keep in mind though that energy is the integral of momentum, so there is a constant that goes missing.
Energy is not conserved like momentum is and it should not be relied on alone in real-world calcs. So given that, I'd call energy a double-derived unit.
What do you mean? Energy isn't conserved at all, or it's conserved differently than momentum?
He's right, in as far as Momentum stays as Momentum but KE is not conserved and can turn up as thermal, electrical etc. which makes it much less useful for dynamics questions, for instance.
Ah I see.
Separate names with a comma.