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için uzun yol, üsün başa düşürülmesi ve bir azaltılmasıyla yapılır.","Kareköklü fonksiyonların türevinin kısayolu: içinden türev bölü iki kök içi şeklinde yazılır.","Kareköklü fonksiyonun türevi hesaplanırken, payda iki ile fonksiyonun aynısı çarpılır, payda ise içindeki ifadenin türevi yazılır."]},"beginTime":145,"endTime":324,"href":"/video/preview/8071602604020154921?parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=Derivative+Stuff+-+Topic&t=145&ask_summarization=1"},{"index":2,"title":"Örnekler ve Uygulamalar","list":{"type":"unordered","items":["Fonksiyonların kuvvetlerinin türevi hesaplanırken, üs başa düşürülüp bir azaltılır ve içindeki ifadenin türevi ile çarpılır.","Türev hesaplamalarında, verilen fonksiyonun türevini bilmek ve kuralı uygulamak önemlidir.","Çeşitli örnekler çözülerek kuralın uygulanması gösterilmiştir."]},"beginTime":324,"endTime":513,"href":"/video/preview/8071602604020154921?parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=Derivative+Stuff+-+Topic&t=324&ask_summarization=1"},{"index":3,"title":"Eksi Kuvvetli Fonksiyonların Türevi","list":{"type":"unordered","items":["Eksi kuvvetli fonksiyonların türevi alırken önce eksi kuvvet durumuna getirilmelidir, örneğin 1/(x²-3x+1)³ ifadesi (x²-3x+1)⁻³ şeklinde yazılmalıdır.","Türev alırken önce üst katsayı indirilir, sonra üst bir azaltılır ve iç fonksiyonun türevi ile çarpılır.","Eksi kuvvetli fonksiyonların türevi alındıktan sonra, eksi kuvvet durumundan dolayı ifade aşağıya indirilebilir."]},"beginTime":515,"endTime":679,"href":"/video/preview/8071602604020154921?parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=Derivative+Stuff+-+Topic&t=515&ask_summarization=1"},{"index":4,"title":"Köklü Fonksiyonların Türevi","list":{"type":"unordered","items":["Köklü fonksiyonların türevi alındığında önce kuvvet durumuna dönüştürülmelidir, örneğin ³√(2x-3)⁵ ifadesi (2x-3)⁵/³ şeklinde yazılmalıdır.","Köklü fonksiyonların türevi alırken üst katsayı indirilir, üst bir azaltılır ve iç fonksiyonun türevi ile çarpılır.","Eksi kuvvetli ve köklü fonksiyonların türevi alındıktan sonra, eksi kuvvet durumundan dolayı ifade aşağıya indirilebilir."]},"beginTime":679,"endTime":860,"href":"/video/preview/8071602604020154921?parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=Derivative+Stuff+-+Topic&t=679&ask_summarization=1"},{"index":5,"title":"Kareköklü Fonksiyonların Türevi İçin Kısa Yol","list":{"type":"unordered","items":["Kareköklü fonksiyonların türevi almak için kısa yol: √f(x) fonksiyonunun türevi 2√f(x) şeklinde yazılır.","Kareköklü fonksiyonların türevinde, kökün içerisindeki fonksiyonun türevi iç kısımda yazılır.","Kareköklü fonksiyonların türevi 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yazılır."]},"beginTime":1169,"endTime":1340,"href":"/video/preview/8071602604020154921?parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=Derivative+Stuff+-+Topic&t=1169&ask_summarization=1"},{"index":7,"title":"Örnek Sorular","list":{"type":"unordered","items":["Beşinci dereceden köklü fonksiyonların türevi hesaplanırken, kuvvet başa düşürülür, üstü bir azaltılır ve iç fonksiyonun türevi ile çarpılır.","Türevin değerini bulmak için x yerine verilen değer yazılır ve hesaplamalar yapılır.","Çarpımın türevi alınırken, çarpım kuralı kullanılır: (f·g)' = f'·g + f·g'."]},"beginTime":1340,"endTime":1759,"href":"/video/preview/8071602604020154921?parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=Derivative+Stuff+-+Topic&t=1340&ask_summarization=1"},{"index":8,"title":"Karmaşık Fonksiyonların Türevi","list":{"type":"unordered","items":["Daha karmaşık fonksiyonların türevi alınırken, önce kuvvet başa düşürülür, sonra üstü bir azaltılır ve iç fonksiyonun türevi ile çarpılır.","İçinde kuvvet olan ifadelerde, kuvvetin türevi alınırken aynı işlem tekrarlanır.","Türev hesaplandıktan sonra, x yerine verilen değer yazılır ve hesaplamalar tamamlanır."]},"beginTime":1759,"endTime":1862,"href":"/video/preview/8071602604020154921?parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=Derivative+Stuff+-+Topic&t=1759&ask_summarization=1"},{"index":9,"title":"Türev Alma Örnekleri","list":{"type":"unordered","items":["Bir türev sorusunun çözümünde hata bulunuyor ve düzeltiliyor.","Bölüm durumunda olan bir fonksiyonun türevi hesaplanıyor: f(x) = (2x+1)³ / (x-1)² türevi bulunuyor.","Kareköklü fonksiyonların türevi alındığında bölümün çekip 2 yazılması ve içindeki fonksiyonun türevinin alınması gerektiği 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derslerinizde başarılar dilerim. By explaining what a derivative is, I introduce the subject of derivatives. In my next videos, I will demonstrate how to take derivatives of function...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/759739/fc339d66d2921298602c4a33aba22b93/564x318_1"},"target":"_self","position":"3","reqid":"1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DpBjRCcx4HI8","linkTemplate":"/video/preview/13733485421698416399?parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=Derivative+Stuff+-+Topic&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Türev nedir ? - What is Derivatives ?","related_orig_text":"Derivative Stuff - Topic","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Derivative Stuff - Topic\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=pBjRCcx4HI8\",\"src\":\"serp\",\"rvb\":\"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_QOCBCQBgAQrKosBEAEaeIH7C_4A_wEA8goFAQMD_gH6CBIE-f79APL6_fwHAf8A9fAJ_P4AAADz_g8F-AAAAPX8CQz0_wEA8vru-gEAAAAI__75_QAAAAP89Qj_AQAA_gEPDgT_AAAQDv39_wAAAP0G9_oCAAAA_gr5CwAAAAAI8_AJAAAAACAALQhh1Ts4E0AJSE5QAipzEAAaYDMYADkXxvDUDAHh9O6-KizfvzD6rfX_ABIA61rICRP03dT33v9Q5BYUowAAADPlxQwaAP1_6sbe-u4s8svY1O5BdhIOHMguEsrhrswBKNP29wVWZgDZ5ff__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_AAAAQgAAmEEAABBCAACAPwAAvsIAAATCAAAcQgAAkEEAAKhBAAAAwAAAJEIAAI7CAAAwQQAAAMEAAPDBAADAQAAAQEEAAMhBAAAUwgAAYMEAAIDAAABQQQAAcMIAAFDCAADwQQAAKMIAAADAAACGwgAAuMEAAODBAAAoQgAAyEEAAKhCAADAQQAAIEEAAADBAABQQQAAIMEAAMBAAACAQAAA2MEAALBBAAAQwgAAEEIAAMZCAAAwwgAAXMIAAGTCAAAIQgAAskIAACjCAABwwgAAMEIAAIC_AACYwQAAQMAAAGTCAABAQQAAwMAAAGDBAACcQgAASMIAAHBBAACAwQAAIMIgADgTQAlIdVABKo8CEAAagAIAAJK-AACAOwAAED0AALg9AADgPAAAFD4AANg9AADavgAA2L0AAI4-AADIvQAA4DwAADA9AABQPQAAmL0AAJg9AAAQPQAAgLsAAIo-AACePgAAfz8AAEC8AADYPQAA4DwAAFy-AAA0vgAABL4AAMi9AACovQAAXD4AADA9AADgPAAA-L0AAAy-AACevgAAsr4AABA9AABMvgAAgr4AAKg9AABQPQAALL4AAKo-AABAvAAAqL0AAHC9AAD4vQAAVL4AAKC8AADYvQAA6D0AAIg9AAD4PQAAiL0AADA9AAAwPQAAFz8AACS-AACoPQAAAT8AAMg9AABAPAAAoLwAAHA9IAA4E0AJSHxQASqPAhABGoACAABUvgAAfD4AAI6-AABVvwAADL4AAIg9AAC2PgAAJL4AAIg9AAAcPgAAMD0AADS-AAC4vQAAfL4AAAw-AABAvAAAED0AABM_AABwvQAAdD4AABC9AACYPQAAiD0AAOC8AABUvgAAoj4AACS-AAAQPQAAyL0AAEy-AAAQPQAAmD0AAOC8AAA8vgAA6L0AABC9AACGPgAAPD4AAGy-AADSvgAAuD0AAGQ-AABwPQAAiD0AAMg9AACGPgAAf78AAFy-AACgvAAADD4AAII-AACYPQAAmj4AAAw-AACAuwAAmD0AAOA8AACovQAALD4AACy-AACGPgAABD4AAMi9AACgvCAAOBNACUh8UAEwCTgBSgBgAGgA\"}","related_url":"http://www.youtube.com/watch?v=pBjRCcx4HI8","parent-reqid":"1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1280,"cheight":720,"cratio":1.77777,"dups":["13733485421698416399"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false},"13332744671078533230":{"videoId":"13332744671078533230","docid":"34-11-0-Z10C8654F08CF3BEA","description":"As we have seen in calculus 1, there are two versions of the definition of the derivative of a function at a, namely f'(a). 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fazlası için: http://www.khanacademy.org.tr Matematikten sanat tarihine, ekonomiden fen bilimlerine, basit toplamadan diferansiyel denklemlere, ilkokul seviyesinden üniversite seviyesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2268062/d745e004352582788a799dfdac63067f/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/qwdnLwAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"9","reqid":"1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=videoid:17434790700513490853","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında bir ders anlatımıdır. Konuşmacı, matematikteki etkileyici sonuçlardan biri olan doğal logaritmanın türevini açıklamaktadır.","Video, e üzeri x'in x'e göre türevinin e üzeri x olduğunu hatırlatarak başlar ve ardından doğal logaritmanın türevini bulma sürecine geçer. Konuşmacı, y = doğal logaritma x denklemini kullanarak zincir kuralı uygulayarak doğal logaritmanın türevinin 1/x olduğunu adım adım gösterir. Video, bu matematiksel sonucun matematikteki etkileyici sonuçlarından biri olduğunu vurgulayarak sona erer."]},"endTime":171,"title":"Doğal Logaritmanın Türevi","beginTime":0}],"fullResult":[{"index":0,"title":"Ters Fonksiyonların Türevi","list":{"type":"unordered","items":["e üzeri x'in x'e göre türevi e üzeri x'e eşittir ve bu matematikte etkileyici bir sonuçtur.","Videoda doğal logaritmanın x'e göre türevi hesaplanacaktır.","Doğal logaritma, e üzeri y = x ifadesinin başka bir yazım şeklidir."]},"beginTime":0,"endTime":51,"href":"/video/preview/17434790700513490853?parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=Derivative+Stuff+-+Topic&t=0&ask_summarization=1"},{"index":1,"title":"Türev Hesaplama","list":{"type":"unordered","items":["e üzeri y = x eşitliğinin her iki tarafının x'e göre türevi alınır.","Sol tarafta zincir kuralı uygulanarak e üzeri y çarpı y'nin x'e göre türevi elde edilir.","Sağ tarafta x'in x'e göre türevi 1'dir."]},"beginTime":51,"endTime":94,"href":"/video/preview/17434790700513490853?parent-reqid=1769647962952524-11272396242584199315-balancer-l7leveler-kubr-yp-sas-243-BAL&text=Derivative+Stuff+-+Topic&t=51&ask_summarization=1"},{"index":2,"title":"Sonuç","list":{"type":"unordered","items":["Denklem çözülerek y'nin x'e göre türevi 1 bölü e üzeri y olarak bulunur.","e üzeri doğal logaritma x ifadesi x'e eşittir çünkü doğal logaritma, e'nin üzerine koyduğumuz kuvvettir.","Sonuç olarak, doğal logaritma x'in x'e göre türevi 1 bölü x'e 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