who directed its video?
Samuel Bayer.
Smells Like Teen Spirit
The music video for "Smells Like Teen Spirit" was the first for director Samuel Bayer. 
who wrote the song smells like teen spirit Kurt Cobain when was it released? 1991
wiki:5384382
Smells Like Teen Spirit [SEP] Music video
The music video for "Smells Like Teen Spirit" was the first for director Samuel Bayer. Bayer believed he was hired because his test reel was so poor the band anticipated his production would be "punk" and "not corporate". The video is based on the concept of a school concert which ends in anarchy and riot, inspired by Jonathan Kaplan's 1979 film "Over the Edge" and the Ramones' film "Rock 'n' Roll High School". It had an estimated budget between $30,000 and $50,000. The video was filmed on August 17, 1991 on Stage 6 of GMT Studios in Culver City. The music video features Nirvana playing at a pep rally in a high school gym to an audience of apathetic students on bleachers, and cheerleaders wearing black dresses with the Circle-A anarchist symbol.