Question: who co-write the song which Taylor Swift videography released its video 
Context: American singer-songwriter Taylor Swift has released four video albums and has appeared in thirty-eight music videos, five films and three television shows.  From her eponymous debut album (2006), she released music videos for the singles "Tim McGraw", "Teardrops on My Guitar", "Our Song", and "Picture to Burn", all directed by Trey Fanjoy and released from 2006–08.  For the second of these, she earned an MTV Video Music Award for Best New Artist nomination.  She followed with three other music videos in 2008—"Beautiful Eyes" from her extended play of the same name, "Change" from the "AT&T Team USA Soundtrack" and "Love Story" from her second album "Fearless" (2008).  The latter was nominated for two awards at the 2009 CMT Music Awards—Video of the Year and Female Video of the Year.  For the video of "You Belong with Me" she won Best Female Video at the 2009 MTV Video Music Awards.  During her acceptance speech, she was interrupted by rapper Kanye West, which sparked controversy and received much media attention. "Teardrops on My Guitar" is a song by American singer-songwriter Taylor Swift.  The song was co-written by Swift, alongside Liz Rose and produced by Nathan Chapman with Swift's aid.  "Teardrops on My Guitar" was released on February 19, 2007 by Big Machine Records, as the second single from Swift's eponymous debut album (2006).  The song was later included on the international release of Swift's second studio album, "Fearless" (2008), and released as the second pop single from the album in the United Kingdom.  It was inspired by Swift's experience with Drew Hardwick, a classmate of hers for whom she had feelings.  He was completely unaware and continually spoke about his girlfriend to Swift, something she pretended to be endeared by.  Years afterwards, Hardwick appeared at Swift's house, but Swift rejected him.  Musically, the track is soft and is primarily guided by a gentle acoustic guitar.  Critics have queried the song's classification as country music, with those in agreement (such as Grady Smith of "Rolling Stone") citing the themes and narrative style as country-influenced and those opposed (such as Roger Holland of "PopMatters") indicating the pop music production and instrumentation lack traditional country elements. Buckethead is an American musician, predominantly a guitarist.  The following is a discography of works by Buckethead, which currently consists of 302 studio albums (including 272 Pikes), 1 live album, 4 special releases, 1 extended play, 5 demo tapes, 3 solo DVD video releases, 2 DVD video releases with Cornbugs, 3 music videos, 3 unreleased albums, 3 solo videography releases, and 16 videography releases with other artists.  Since 1994, Buckethead has released 6 studio efforts under the anagram of Death Cube K.  He has released 74 works with other bands and artists (including his work as Death Cube K).  The total number of studio albums, special releases, extended plays, demo tapes, and works with other bands and projects is 378.  His guest appearances total 97.  His videography releases total 19.  In total, Buckethead has been involved with 475 different album projects (as solo or with other bands).  As of his 300th solo studio album, A3, his total solo studio album running time is approximately 159.02 hours. The 2015 MTV Video Music Awards were held on August 30, 2015.  The 32nd installment of the event was held at the Microsoft Theater in Los Angeles, California, and hosted by Miley Cyrus.  Taylor Swift led the nominations with a total of ten, followed by Ed Sheeran, who had six., bringing his total number of mentions to 13.  Swift's "Wildest Dreams" music video premiered during the pre-show.  Cyrus also announced and released her studio album "Miley Cyrus & Her Dead Petz", right after her performance at the end of the show.  During his acceptance speech, Kanye West announced that he would be running for the 2020 U.S. Presidential Election.  Taylor Swift won the most awards with four, including Video of the Year and Best Female Video.  The VMA trophies were redesigned by Jeremy Scott. "Fearless" is a country pop song performed by American singer-songwriter Taylor Swift.  The song was co-written by Swift in collaboration with Liz Rose and Hillary Lindsey and produced by Nathan Chapman and Swift.  "Fearless" was released on January 3, 2010 by Big Machine Records as the fifth and final single from Swift's second studio album of the same name (2008).  Swift composed the song while traveling on tour to promote her eponymous debut album, "Taylor Swift" (2006).  She wrote "Fearless" in regard to the fearlessness of falling in love and eventually titled her second studio album after the song.  Musically, it contains qualities commonly found in country pop music and, lyrically, is about a perfect first date. "Picture to Burn" is a song recorded by American singer-songwriter Taylor Swift.  It was co-written by Swift and Liz Rose, and produced by Nathan Chapman.  It was released on February 3, 2008 by Big Machine Records as the fourth single from Swift's eponymous studio album, "Taylor Swift" (2006).  It was inspired by the narcissistic and cocky nature of her former high school classmate and ex-boyfriend Jordan Alford with whom Swift never established a formal relationship.  In retrospect, Swift has stated that she has evolved on a personal level and as a songwriter, claiming she processed emotions differently since "Picture to Burn".  The song was chosen as a single based on the audience's reaction to it in concert.  Musically, the track is of the country rock genre with prominent usage of guitar, banjo, and drums.  The lyrics concern setting fire to photographs of a former boyfriend. "Our Song" is a country song performed by American singer-songwriter Taylor Swift.  The song was written by Swift and produced by Nathan Chapman.  It was released on September 9, 2007 by Big Machine Records as the third single from Swift's eponymous debut album, "Taylor Swift" (2006).  Swift solely composed "Our Song" for the talent show of her freshman year in high school, about a boyfriend who she did not have a song with.  It was included on "Taylor Swift" as she recalled its popularity with her classmates.  The uptempo track is musically driven mainly by banjo and lyrically describes a young couple who use the events in their lives in place of a regular song. The Taylor Swift Holiday Collection, originally titled Sounds of the Season: The Taylor Swift Holiday Collection, is a Christmas EP by American singer Taylor Swift.  The EP was first released on October 14, 2007 by Big Machine Records exclusively to Target stores in the United States and online.  The release was originally a limited release for the 2007 holiday season, but was re-released to iTunes and Amazon.com on December 2, 2008 and again in October 2009 to Target stores.  "The Taylor Swift Holiday Collection" features cover versions of Christmas songs and two original tracks written by Swift, "Christmases When You Were Mine" and "Christmas Must Be Something More", all of which have a country pop sound. Beautiful Eyes is the second extended play (EP) by American singer-songwriter Taylor Swift.  The EP was released on July 15, 2008 by Big Machine Records exclusively to Walmart stores in the United States and online.  The limited release EP has a primarily country pop sound and features alternate versions of tracks from her debut album, "Taylor Swift" (2006), and two original tracks, "Beautiful Eyes" and "I Heart ?" , songs which she had previously written; a DVD, featuring music videos of singles from "Taylor Swift", is also included on the physical release of the EP. Taylor Swift is the debut studio album by American singer-songwriter Taylor Swift, released on October 24, 2006, by Big Machine Records.  Swift was 16 years old at the time of the album's release and wrote its songs during her freshman year of high school.  Swift has writing credits on all of the album's songs, including those co-written with Liz Rose.  Swift experimented with several producers, ultimately choosing Nathan Chapman, who had produced her demo album.  Musically, the album is country music styled, and lyrically it speaks of romantic relationships, a couple of which Swift wrote from observing relationships before being in one.  Lyrics also touch on Swift's personal struggles in high school.
Answer: Swift and Liz Rose