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#fonksiyonkuvvetitürevi #aytmatematik fonksiyonun kuvvetinin türevi, bileşke fonksiyonun türevi,türev ,türev alma kuralları, bileşke fonksiyonun türevi, türev konu anlatımı , türev soru...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4362296/12d329c14a176dfb33e10300cedc6187/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/aU62KAIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"7","reqid":"1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=videoid:8071602604020154921","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin türev konusunu anlattığı kapsamlı bir eğitim içeriğidir. Öğretmen, öğrencilere hitap ederek konuyu adım adım açıklamaktadır.","Videoda fonksiyonların kuvvetlerinin türevi, eksi kuvvetlerin türevi ve köklü fonksiyonların türevi gibi temel türev alma kuralları detaylı olarak ele alınmaktadır. Öğretmen önce genel kuralları anlatıp, ardından kareköklü, küp köklü ve beş dereceden köklü fonksiyonların türevlerini hesaplama yöntemlerini örneklerle göstermektedir.","Video boyunca 82. sorudan başlayarak 86. soruya kadar çeşitli türev problemleri çözülmekte ve \"bölü çek iki yaz\" gibi pratik kısayol yöntemleri açıklanmaktadır. Öğretmen, bir sonraki videoda f² fonksiyonunun türevleri ve zincir kuralını işleyeceğini belirtmekte, ayrıca türev alma kurallarının son üçünün parçalı fonksiyon ve mutlak değer fonksiyonu türevleri olacağını ifade etmektedir."]},"endTime":2476,"title":"Türev Dersi: Fonksiyonların Kuvvetlerinin Türevi","beginTime":0}],"fullResult":[{"index":0,"title":"Fonksiyonların Kuvvetlerinin Türevi","list":{"type":"unordered","items":["Bir fonksiyonun karesi, küpü veya başka bir kuvvetinin türevini alırken, önce üs başa düşürülür.","Üs bir azaltılır ve fonksiyonun kendisi olduğu gibi yazılır.","Son olarak, fonksiyonun içindeki ifadenin türevi ile çarpılır."]},"beginTime":33,"endTime":145,"href":"/video/preview/8071602604020154921?parent-reqid=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&t=33&ask_summarization=1"},{"index":1,"title":"Kareköklü Fonksiyonların Türevi","list":{"type":"unordered","items":["Kareköklü fonksiyonların türevi 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=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&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=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&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=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&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=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&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 alındığında, katsayılar ve kök içindeki fonksiyonun türevi hesaplanarak sonuç elde edilir."]},"beginTime":860,"endTime":1161,"href":"/video/preview/8071602604020154921?parent-reqid=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&t=860&ask_summarization=1"},{"index":6,"title":"Köklü Fonksiyonların Türevi","list":{"type":"unordered","items":["Küp köklü, kareköklü ve beşinci dereceden köklü fonksiyonların türevi hesaplanıyor.","Küp köklü fonksiyonların türevi için önce kuvvet başa düşürülür, sonra üstü bir azaltılır ve iç fonksiyonun türevi ile çarpılır.","Kareköklü fonksiyonların türevi için karekök işaretinin altındaki ifadenin türevi alınır ve kökün derecesi (2) payda olarak yazılır."]},"beginTime":1169,"endTime":1340,"href":"/video/preview/8071602604020154921?parent-reqid=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&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=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&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=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&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 hatırlatılıyor."]},"beginTime":1872,"endTime":2086,"href":"/video/preview/8071602604020154921?parent-reqid=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&t=1872&ask_summarization=1"},{"index":10,"title":"Kareköklü Fonksiyonların Türevi","list":{"type":"unordered","items":["f(x) = √(x² + √(x+3)) fonksiyonunun türevi hesaplanıyor.","Kareköklü fonksiyonların türevi alındığında bölümün çekip 2 yazılması ve içindeki fonksiyonun türevinin alınması gerektiği tekrarlanıyor.","f(x) = √(2x+6) / 5 fonksiyonunun türevi hesaplanıyor."]},"beginTime":2086,"endTime":2355,"href":"/video/preview/8071602604020154921?parent-reqid=1769547494235732-146287652034660872-balancer-l7leveler-kubr-yp-klg-233-BAL&text=Derivative&t=2086&ask_summarization=1"},{"index":11,"title":"Çarpım ve Türev Kullanımı","list":{"type":"unordered","items":["f(x) = √(g(x)·h(x)) fonksiyonunun türevi hesaplanıyor.","Çarpımın türevi formülü kullanılarak g'(x)·h(x) + g(x)·h'(x) ifadesi elde ediliyor.","Türev alma kuralları konusunda önemli başlıklar işleniyor ve bundan sonraki videoda f²(x) fonksiyonlarının türevleri ve zincir kuralı ele 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to all of you who support me on Patreon. 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