A Derivative is a character based on existing ones.
The term "Derivative" is sometimes difficult to explain and conceptualize. The overseas often call such characters "fan mades" or "fan made characters", but refer to them as different characters in their own right. However, in the Japanese fandom, the character is often considered a variation of the original (for example, perceiving Yowane Haku as Hatsune Miku with a bad singing voice). Therefore there is often disparity between fandoms as to how 'Derivatives' are treated.
This also means official derivatives like "Racing Miku " or "Snow Miku " can also be considered a variation of Hatsune Miku and at the same time not Hatsune Miku herself. This way, derivative versions of a character can exist side by side in any promotional media base medium with the original character as two
different entities to each other, rather than just alternate outfits.
Crypton Future Media is the most known out of the studios for adopting official derivatives into their merchandise. Derivatives are therefore welcome and often developed as a person's interpretation of the Vocaloid they are working with. Many are used by Producers as a form of self-promotion and are taken into account for the number of such designs and appearances in Vocaloid media. If the song is used officially by Crypton Future Media, the Producer's derivative design is also used in the song alongside it. Crypton Future Media consider them a form of Producer creativity and have adopted the most famous ones into their official character promotions.
However, the sheer number of derivatives that have been produced, particularly in the early 2007-2009 period, have resulted in common generic Vocaloid design traits being acknowledged.