I came so late...
資格外活動許可(Permission to Engage in an Activity Other Than That Permitted by the Status of Residence Previously Granted)
28 hours a week.
respective approval has to be acquired at each job change (in dependent visa).
there is no fee for permission.
Immigration Procedures Guidebook
http://www.moj.go.jp/ONLINE/IMMIGRATION/16-8-1.pdf(an application form)