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üniversite matematiği derslerinden calculus-I dersine ait \"Türev Kuralları\" videosudur. Hazırlayan: Kemal Duran (Matematik Öğretmeni) http://www.buders.com/kadromuz.html adresinden...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3382530/eb85c7b6010d4bedd315263db26e1d57/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/Kb68zAAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"1","reqid":"1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=videoid:2528762654467065836","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan matematik eğitimi formatında hazırlanmış kapsamlı bir ders anlatımıdır.","Video, türevin sembolsel gösterimlerinden başlayarak toplam on türev kuralını detaylı şekilde ele almaktadır. İlk beş kural sabit sayıların, doğrusal fonksiyonların, x üzeri n formatındaki fonksiyonların, toplama-çıkarma durumundaki ifadelerin ve parantezli fonksiyonların türevlerini kapsamaktadır. Daha sonra üstel fonksiyonlar, logaritmalar ve trigonometrik fonksiyonların türev kuralları anlatılmakta, son olarak ters trigonometrik fonksiyonların türevleri ve \"gizli parantez\" durumları açıklanmaktadır.","Video, her kuralın ardından örnekler çözülerek konuyu pekiştirmekte ve çarpım ve bölümün türevi ile özel türev alma kurallarının ayrı videolarda işleneceği bilgisiyle sonlanmaktadır."]},"endTime":3220,"title":"Türev Kuralları Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Türev Sembolleri","list":{"type":"unordered","items":["Türev kuralları, türevin işlemsel sürecini temsil eden kuralları içerir.","Bir fonksiyonun türevi, çentik işaretiyle (f') veya d/dx sembolüyle gösterilir.","Türevin derecesi çentik sayısıyla veya d/dx'in üstündeki üsle gösterilir, örneğin f'' ikinci türevi, f⁽⁴⁾ dördüncü türevi temsil eder."]},"beginTime":1,"endTime":180,"href":"/video/preview/2528762654467065836?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=1&ask_summarization=1"},{"index":1,"title":"Türev Kuralları","list":{"type":"unordered","items":["Sabit sayının türevi sıfırdır (d/dx c = 0).","f(x) = ax fonksiyonunun türevi x'in katsayısı olan a'dır (f'(x) = a).","f(x) = xⁿ formatındaki fonksiyonların türevi n·xⁿ⁻¹ formülüyle hesaplanır."]},"beginTime":180,"endTime":549,"href":"/video/preview/2528762654467065836?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=180&ask_summarization=1"},{"index":2,"title":"Toplama-Çıkarma ve Parantez Türev Kuralları","list":{"type":"unordered","items":["Toplama-çıkarma durumundaki ifadelerin türevi ayrı ayrı alınır.","Parantezli fonksiyonların türevi, parantezin dışındaki üsün üstüne geçip bir azalması ve içerideki fonksiyonun türeviyle çarpılarak 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Türevi","list":{"type":"unordered","items":["Logaritmalar ikiye ayrılır: ln(g(x)) (tabanı e olan logaritma) ve log_a(g(x)) (tabanı e dışında bir sayı olan logaritma).","ln(g(x))'in türevi g'(x) bölü g(x)'dir.","f(x) = ln(x) türevi 1/x'dir.","f(x) = ln(x+1) türevi 2x/(x+1)'dir.","f(x) = ln(4x-7) türevi 4/(4x-7)'dir."]},"beginTime":1545,"endTime":1717,"href":"/video/preview/2528762654467065836?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=1545&ask_summarization=1"},{"index":7,"title":"log_a(g(x)) Fonksiyonlarının Türevi","list":{"type":"unordered","items":["log_a(g(x))'in türevi g'(x) bölü g(x) çarpı ln(e)/ln(a)'dır.","f(x) = log_3(2x+1) türevi 2/(2x+1) çarpı ln(e)/ln(3)'dur.","f(x) = log_5(x^2+x-1) türevi (2x+1)/(x^2+x-1) çarpı ln(e)/ln(5)'dir."]},"beginTime":1717,"endTime":1826,"href":"/video/preview/2528762654467065836?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=1717&ask_summarization=1"},{"index":8,"title":"Trigonometrik Fonksiyonların Türevi","list":{"type":"unordered","items":["sin(g(x))'in türevi cos(g(x)) çarpı g'(x)'dir.","f(x) = sin(x) türevi cos(x)'dir.","f(x) = sin(4x) türevi 4cos(4x)'dir.","f(x) = sin(x^2+1) türevi cos(x^2+1) çarpı 2x'dir."]},"beginTime":1826,"endTime":1948,"href":"/video/preview/2528762654467065836?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=1826&ask_summarization=1"},{"index":9,"title":"Kosinüs ve Tanjant Fonksiyonlarının Türevi","list":{"type":"unordered","items":["cos(g(x))'in türevi -sin(g(x)) çarpı g'(x)'dir.","f(x) = cos(4x) türevi -4sin(4x)'dir.","f(x) = cos(e^(5x)) türevi -e^(5x)sin(e^(5x)) çarpı 5e^(5x)'dır.","f(x) = cos(ln(x^3)) türevi -sin(ln(x^3)) çarpı 3x^2/x^3'dür."]},"beginTime":1948,"endTime":2112,"href":"/video/preview/2528762654467065836?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=1948&ask_summarization=1"},{"index":10,"title":"Tanjant Fonksiyonunun Türevi","list":{"type":"unordered","items":["tan(g(x))'in türevi 1 + tan^2(g(x)) çarpı g'(x)'dir.","Alternatif olarak tan(g(x))'in türevi sec^2(g(x)) çarpı g'(x) veya 1/cos^2(g(x)) çarpı g'(x)'dir.","f(x) = tan(4x) türevi (1 + tan^2(4x)) çarpı 4'dür.","f(x) = tan(e^(3x)) türevi (1 + tan^2(e^(3x))) çarpı 3e^(3x)'dır."]},"beginTime":2112,"endTime":2258,"href":"/video/preview/2528762654467065836?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=2112&ask_summarization=1"},{"index":11,"title":"Kotanjantın Türevi","list":{"type":"unordered","items":["Kotanjantın türevi için üç alternatif formül vardır: -1/(g(x)²) + cot²(g(x))g'(x), -cosec²(g(x))g'(x) ve -1/sin²(g(x))g'(x).","Cosecant (csc) fonksiyonu 1/sin olarak tanımlanır ve bazı kaynaklarda csc şeklinde yazılır.","Kotanjantın türevi genellikle -cosec²(g(x))g'(x) veya -1/sin²(g(x))g'(x) şeklinde hatırlanabilir."]},"beginTime":2267,"endTime":2429,"href":"/video/preview/2528762654467065836?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=2267&ask_summarization=1"},{"index":12,"title":"Sekant ve Kosekantın Türevi","list":{"type":"unordered","items":["Sekantın türevi sec(g(x))tan(g(x))g'(x) formülüyle hesaplanır.","Kosekantın türevi -csc(g(x))cot(g(x))g'(x) formülüyle hesaplanır.","Trigonometrik fonksiyonların türev kuralları bu şekilde tamamlanmıştır."]},"beginTime":2429,"endTime":2591,"href":"/video/preview/2528762654467065836?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=2429&ask_summarization=1"},{"index":13,"title":"Ters Trigonometrik Fonksiyonların Türevi","list":{"type":"unordered","items":["Arksin(g(x))'in türevi g'(x)/√(1-g(x)²) formülüyle hesaplanır.","Arkcos(g(x))'in türevi -g'(x)/√(1-g(x)²) formülüyle hesaplanır.","Arctan(g(x))'in türevi g'(x)/(1+g(x)²) formülüyle hesaplanır.","Arkcot(g(x))'in türevi -g'(x)/(1+g(x)²) formülüyle hesaplanır."]},"beginTime":2591,"endTime":2945,"href":"/video/preview/2528762654467065836?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=2591&ask_summarization=1"},{"index":14,"title":"Gizli Parantezlerin Türevi","list":{"type":"unordered","items":["Gizli parantezler, türevi alırken parantezli olarak ele alınması gereken ifadelerdir.","(f(x))^n ifadelerinde türev alırken üstü başa getirip bir azaltır, sonra içerideki fonksiyonun türevini alırız.","Örneğin, sin²(x) türevi 2sin(x)cos(x), cos²(x) türevi -2sin(x)cos(x), ln²(x) türevi 2ln(x)/x ve tan³(x) türevi 3tan²(x)sec²(x) 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Hazırlayan: Kemal Duran (Matematik Öğretmeni) http://www.buders.com/kadromuz.html...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3219019/d2e10e33cb6f0df526bbda46532065e2/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/MEtRAAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"3","reqid":"1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=videoid:5139934214424500319","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında mutlak değerli fonksiyonların türevini anlatan bir ders anlatımıdır.","Video, mutlak değerli fonksiyonların türev kuralını açıklayarak başlıyor ve ardından bu kuralı örneklerle pekiştiriyor. Mutlak değerli fonksiyonun türevi, mutlak değerin içinin türevi ile mutlak değerin kendisi çarpımıdır. Videoda üç farklı örnek üzerinden türev hesaplamaları gösteriliyor ve son olarak mutlak değerin içini sıfır yapan noktalarda türevin olmadığı bilgisi veriliyor."]},"endTime":430,"title":"Mutlak Değerli Fonksiyonların Türevi","beginTime":0}],"fullResult":[{"index":0,"title":"Mutlak Değerli Fonksiyonların Türevi","list":{"type":"unordered","items":["Mutlak değerli fonksiyonların türevi, mutlak değerin içindeki fonksiyonun türevi ile mutlak değerin kendisinin çarpımına eşittir.","Mutlak değerli fonksiyonun türev kuralı: f(x) = |g(x)| ise f'(x) = g'(x) × |g(x)| / g(x) şeklindedir.","Mutlak değerli fonksiyonun içindeki g(x) değeri, pozitifse +1, negatifse -1 olarak dışarı çıkar."]},"beginTime":1,"endTime":105,"href":"/video/preview/5139934214424500319?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=1&ask_summarization=1"},{"index":1,"title":"Örnekler","list":{"type":"unordered","items":["Örnek 1: f(x) = |x³ + 1| fonksiyonunun türevi f'(x) = 3x² × |x³ + 1| / (x³ + 1) şeklindedir.","Örnek 2: f(x) = |x³ + x² + 3x - 1| fonksiyonunun f'(-2) değeri -11 olarak hesaplanır.","Örnek 3: f(x) = |x² + 3x| fonksiyonunun f'(1) değeri 5 olarak bulunur."]},"beginTime":105,"endTime":359,"href":"/video/preview/5139934214424500319?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=105&ask_summarization=1"},{"index":2,"title":"Mutlak Değerli Fonksiyonların Türevi İçin Önemli Bir Özellik","list":{"type":"unordered","items":["Mutlak değerin içindeki ifadeyi sıfır yapan x değerinde türev yoktur.","Mutlak değerin içindeki ifadeyi sıfır yapan değer, türev formülündeki payda sıfır yaparak tanımsızlığa neden olur.","Örneğin, f(x) = |x - 3| fonksiyonunun x = 3 noktasında türevi 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Hazırlayan: Kemal Duran (Matematik Öğretmeni)...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3829577/bada03e826a2946215c69c560bde6d03/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/0SZAUwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"5","reqid":"1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=videoid:7059321714531892460","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan Calculus dersinde fonksiyon grafiklerinin nasıl çizileceğini anlatan eğitim içeriğidir.","Video, türev kullanarak fonksiyon grafiği çizmenin yedi adımlı bir yöntemini detaylı şekilde açıklamaktadır. Bu adımlar sırasıyla tanım kümesi bulma, eksenleri kestiği noktaları belirleme, asimptotları bulma, limit hesaplamaları, birinci türevi alıp maksimum-minimum noktaları bulma, ikinci türevi alıp bükeylik aralıklarını belirleme ve son olarak grafik çizme olarak sıralanmaktadır. Eğitmen, bu adımları bir kesirli fonksiyon örneği üzerinden uygulamalı olarak göstermektedir.","Video, bir serinin parçası olup, beş-altı bölümden oluşacağını belirtmektedir. Bir sonraki videoda düşey asimptotların sağdan-soldan yaklaşma durumunun grafik çizimindeki kullanımı gösterilecektir. Eğitmen ayrıca kesirsiz fonksiyonlar için de benzer içerikler hazırlayacağını belirtmektedir."]},"endTime":2660,"title":"Türev Kullanarak Fonksiyon Grafiği Çizme Eğitimi","beginTime":0}],"fullResult":[{"index":0,"title":"Türev Kullanarak Fonksiyon Grafiği Çizme","list":{"type":"unordered","items":["Türev kullanarak fonksiyon grafiği çizme, Calculus 1'de en önemli başlıklarından biridir ve sınavlarda mutlaka sorulur.","Fonksiyon grafiği çizme yedi adımdan oluşur ve bu adımları sırasıyla uygulamak gerekir.","Bazı üniversiteler soruyu sadece fonksiyonu verip grafiğini çiziniz diye sorarken, diğerleri adımları şıkk halinde yönlendirerek sorar."]},"beginTime":0,"endTime":75,"href":"/video/preview/7059321714531892460?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=0&ask_summarization=1"},{"index":1,"title":"Fonksiyon Grafiği Çizme Adımları","list":{"type":"unordered","items":["Birinci adım: Fonksiyonun tanım kümesi (domain) bulunmalıdır.","İkinci adım: Fonksiyonun x ve y eksenlerini kestiği noktalar bulunmalıdır.","Üçüncü adım: Asimptotlar (düşey, yatay ve eğik asimptotlar) bulunmalıdır."]},"beginTime":75,"endTime":240,"href":"/video/preview/7059321714531892460?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=75&ask_summarization=1"},{"index":2,"title":"Asimptotlar ve Limitler","list":{"type":"unordered","items":["Asimptotlar kesirli fonksiyonlarda bulunur, kesirsiz fonksiyonlarda (polinomlarda) asimptotlar yoktur.","Dördüncü adım: Düşey asimptota sağdan ve soldan limitler hesaplanmalıdır.","Düşey asimptotun İngilizcesi vertical asimptot, yatay asimptot horizontal asimptot, eğik asimptot ise oblique 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çizmeliyiz.","Ardından maksimum-minimum noktaları ve büküm noktalarını yerleştirmeliyiz.","Son olarak x ve y eksenlerini kestiği noktaları yerleştirdikten sonra, artan-azalan ve bükeylik bilgilerine göre çizim yapmalıyız."]},"beginTime":564,"endTime":698,"href":"/video/preview/7059321714531892460?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=564&ask_summarization=1"},{"index":5,"title":"Örnek Çözüm","list":{"type":"unordered","items":["Örnek olarak f(x) = (x-1)/(x+1) fonksiyonunun grafiğini çizeceğiz.","Tanım kümesi bulmak için paydayı sıfır yapan x değerleri bulunur, bu örnekte x ≠ -1 olduğundan tanım kümesi tüm reel sayılardır.","Y eksenini kestiği nokta x=0 için f(0) = -1'dir, x eksenini kestiği noktalar ise f(x)=0 için x = ±1'dir."]},"beginTime":698,"endTime":960,"href":"/video/preview/7059321714531892460?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=698&ask_summarization=1"},{"index":6,"title":"Fonksiyonun Asimptotları","list":{"type":"unordered","items":["Fonksiyonun düşey asimptotu yok çünkü paydayı sıfır yapan x değeri bulunmuyor.","Yatay asimptot, fonksiyonun x eksi ve artı sonsuza giderken limit değeridir ve bu örnekte y=1'dir.","Düşey asimptot olmadığı için 4. adımda sağdan ve soldan limit hesaplaması yapılmaz."]},"beginTime":972,"endTime":1133,"href":"/video/preview/7059321714531892460?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=972&ask_summarization=1"},{"index":7,"title":"Birinci Türev ve Artan-Azalan Aralıklar","list":{"type":"unordered","items":["Fonksiyonun birinci türevi alınarak f'(x) = 4x / (x²+1)² elde edilir.","Birinci türev sıfır yapan değer x=0'dır ve 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Teğet doğrunun eğiminin teğet olunan noktada fonksiyonun türevine eşit olduğu, teğet doğrusunun denkleminin nasıl yazılacağı ve kapalı fonksiyonlarda türev alma kuralları gibi konular ele alınıyor. Video, sınavlarda sıkça sorulan bu konunun temel kavramlarını ve uygulamalarını içermektedir."]},"endTime":1025,"title":"Teğetin Eğimi ve Denklemi Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Teğet Doğrunun Eğimi ve Denklemi","list":{"type":"unordered","items":["Teğet doğrunun eğimi, teğet olunan noktada fonksiyonun türevine eşittir.","Türev, bir fonksiyonun y değerlerinin x değerlerine göre değişim hızını gösterir.","Teğet doğrunun denklemi yazabilmek için doğru üzerinde bir nokta ve eğim gerekir."]},"beginTime":0,"endTime":333,"href":"/video/preview/2827674753179409198?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=0&ask_summarization=1"},{"index":1,"title":"Teğet Doğrunun Denklemi Formülü","list":{"type":"unordered","items":["Doğru denklemi formülü: y-y₁ = m(x-x₁) şeklindedir, burada m eğimi, (x₁,y₁) doğrunun geçtiği noktayı temsil eder.","Teğet olunan noktada fonksiyonun türevini alıp o noktayı 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Hazırlayan: Kemal Duran (Matematik Öğretmeni)...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3829577/bada03e826a2946215c69c560bde6d03/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/gRt0LgAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"9","reqid":"1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=videoid:7882359563724675361","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında bir ders anlatımıdır. Eğitmen, disk metodu ile hacim hesaplama konusunu üç video serisi olarak ele almaktadır.","Video, disk metodu ile hacim hesaplamasının ilk bölümünü oluşturmaktadır. İçerikte x ekseni etrafında döndürme durumunda hacim hesaplama için iki farklı durum incelenmektedir: alanın x eksenine teması olan durum ve teması olmayan durum (washer metodu). Eğitmen, her iki durum için formülleri açıklamakta ve bunları iki örnek soru üzerinden uygulamalı olarak göstermektedir. Video, disk metodu ile hacim hesaplama konusunu öğrenmek isteyenler için temel bilgileri içermektedir."]},"endTime":989,"title":"Disk Metodu ile Hacim Hesaplama: X Ekseni Etrafında Döndürme","beginTime":0}],"fullResult":[{"index":0,"title":"Disk Metodu ile Hacim Hesaplama","list":{"type":"unordered","items":["Disk metodu ile hacim hesaplaması üç video olarak incelenecek: x ekseni etrafında döndürme, y ekseni etrafında döndürme ve bir doğru etrafında döndürme.","Disk metodu ile x ekseni etrafında döndürme hesaplaması iki farklı durumda yapılır.","Hacmin oluşabilmesi için bir alanın eksen etrafında döndürülmesi gerekir."]},"beginTime":1,"endTime":65,"href":"/video/preview/7882359563724675361?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=1&ask_summarization=1"},{"index":1,"title":"Disk Metodunun Çeşitleri","list":{"type":"unordered","items":["Birinci durum: Döndürülen alanın x eksenine teması olan durum.","İkinci durum: Döndürülen alanın x eksenine teması olmayan durum, bu durumda washer metodu adı verilir.","Washer metodu, disk metodunun bir alt başlığıdır."]},"beginTime":65,"endTime":173,"href":"/video/preview/7882359563724675361?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=65&ask_summarization=1"},{"index":2,"title":"Hacim Hesaplama Formülleri","list":{"type":"unordered","items":["Alanın x eksenine teması varken hacim formülü: V = π∫[a,b] (f(x))^2 dx'dir.","Alanın x eksenine teması yokken hacim formülü: V = π∫[a,b] ((üst fonksiyon)^2 - (alt fonksiyon)^2) dx'dir.","Hacim hesaplamasında alanın doğru çizilmesi ve analiz edilmesi önemlidir."]},"beginTime":173,"endTime":361,"href":"/video/preview/7882359563724675361?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=173&ask_summarization=1"},{"index":3,"title":"Örnek Sorular","list":{"type":"unordered","items":["Soruda yöntem 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İlk adım, teğet doğrunun eğimini bulmak için dy/dx türevini hesaplamaktır. İkinci adım, teğet noktasının kartezyen koordinatlarını (x, y) bulmaktır. Üçüncü adım ise doğru denklemi yazma formülü kullanarak teğet doğrunun denklemini yazmaktır. Video, bu adımları bir örnek sorusu üzerinden uygulamalı olarak göstermektedir."]},"endTime":702,"title":"Kutupsal Koordinatlarda Teğet Doğru Denklemi Bulma","beginTime":0}],"fullResult":[{"index":0,"title":"Kutupsal Koordinatlarda Teğet Doğru Denklemi","list":{"type":"unordered","items":["Bu videoda kutupsal koordinatlarda verilen bir eğriye belli bir noktada çizilen teğet doğrunun denklemi nasıl bulunur.","Kutupsal koordinatlarda verilen bir eğri r = f(θ) şeklinde ifade edilir ve çeşitli grafikler olabilir.","Teğet doğrunun denklemi kartezyen koordinatlarda bulunacağından, kutupsal koordinatları kartezyen koordinatlara dönüştürmek gerekir."]},"beginTime":0,"endTime":141,"href":"/video/preview/13413170013109945259?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=0&ask_summarization=1"},{"index":1,"title":"Teğet Doğru Denklemini Bulma Adımları","list":{"type":"unordered","items":["Birinci adım: dy/dx türevini hesaplayıp θ 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konu anlatımı ve soru çözümü videoları için: • Calculus - Kuzey Kampüs ne tür videolar ol... • Calculus 1 Limit Soru Çözümü 3. Ders Lim... 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Eğitmen, tek değişkenli fonksiyonların belirli bir noktada lineer yaklaşımını nasıl bulabileceğimizi, teğet doğrularla yaklaşım mantığını ve yaklaşık değer hesabı yapma yöntemlerini açıklamaktadır. İki örnek üzerinden (x+1)^3 ve (x+1)^2 fonksiyonları için lineer yaklaşım bulma süreci gösterilmekte ve yaklaşık değer hesaplamaları anlatılmaktadır. 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Hazırlayan: Kemal Duran (Matematik Öğretmeni)...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3219019/d2e10e33cb6f0df526bbda46532065e2/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/IM5SBgEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"15","reqid":"1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=videoid:3853625895084701349","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan matematik eğitimi formatında kapalı fonksiyonların türevi konusunu anlatan bir ders anlatımıdır.","Video, kapalı fonksiyonların ne olduğunu açıklayarak başlıyor ve y'nin yalnız bırakılamadığı fonksiyonların kapalı fonksiyon olduğunu örneklerle gösteriyor. Ardından kapalı fonksiyonların türevinin nasıl alınacağı adım adım anlatılıyor: her iki tarafın x'e göre türevi alınır, y'li ifadeler x'e bağlı fonksiyonlar olarak kabul edilir ve türevleri alınır. Video, bu kuralları iki farklı örnek üzerinden uygulamalı olarak gösteriyor.","Örnekler arasında x² + y³ = e^(xy) - 4 gibi daha karmaşık fonksiyonlar da bulunmaktadır. Her iki örnekte de y türevini yalnız bırakma adımı detaylı olarak açıklanmaktadır."]},"endTime":1328,"title":"Kapalı Fonksiyonların Türevi Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Kapalı Fonksiyon Nedir?","list":{"type":"unordered","items":["Kapalı fonksiyonun İngilizcesi \"implicit differentiation\" (kapalı türev) olarak ifade edilir.","Kapalı fonksiyon, y değerinin yalnız bırakılamayan fonksiyonlardır.","Kapalı fonksiyonlar f(x) şeklinde ifade edilemez, f(x,y) şeklinde ifade edilirler."]},"beginTime":1,"endTime":87,"href":"/video/preview/3853625895084701349?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=1&ask_summarization=1"},{"index":1,"title":"Kapalı Fonksiyon Örnekleri","list":{"type":"unordered","items":["x² + y² = 1 gibi fonksiyonlarda y yalnız bırakılamaz çünkü y² = ±√(1-x²) olur ve y'nin değerinin pozitif mi yoksa negatif mi olduğu belirsiz kalır.","x + y², x²y³ + 3xy - 4x + 5y² + e^x gibi fonksiyonlar da kapalı fonksiyonlardır.","y yalnız bırakılabiliyorsa normal fonksiyon, yalnız bırakılamıyorsa kapalı fonksiyondur."]},"beginTime":87,"endTime":222,"href":"/video/preview/3853625895084701349?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=87&ask_summarization=1"},{"index":2,"title":"Kapalı Fonksiyonların Türevi","list":{"type":"unordered","items":["Kapalı fonksiyonların türevi alırken her iki tarafın da x'e göre türevi alınır.","Kapalı fonksiyonlarda y, x'e bağlı bir fonksiyon olarak kabul edilir ve türev alınırken bu durum dikkate alınmalıdır.","Yalnız y'nin türevi dy/dx olarak ifade edilir, y²'nin türevi 2y(dy/dx), y³'nin türevi 3y²(dy/dx) şeklinde hesaplanır."]},"beginTime":222,"endTime":536,"href":"/video/preview/3853625895084701349?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=222&ask_summarization=1"},{"index":3,"title":"Kapalı Fonksiyon Türevi Örneği","list":{"type":"unordered","items":["x + y² = 5 kapalı fonksiyonunda her iki tarafın da x'e göre türevi alınır.","Türev alındıktan sonra dy/dx yalnız bırakılarak kapalı fonksiyonun türevi bulunur.","Örnek sonucunda dy/dx = -x/y olarak hesaplanır."]},"beginTime":536,"endTime":725,"href":"/video/preview/3853625895084701349?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=536&ask_summarization=1"},{"index":4,"title":"Kapalı Fonksiyonların Türevi","list":{"type":"unordered","items":["Kapalı fonksiyonlar, y'yi yalnız bırakılamayan fonksiyonlardır.","Kapalı fonksiyonların türevi alırken her iki tarafın x'e göre türevini almak gerekir.","Türev alma işleminden sonra y'nin türevi (dy/dx) yalnız bırakılmalıdır."]},"beginTime":747,"endTime":773,"href":"/video/preview/3853625895084701349?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=747&ask_summarization=1"},{"index":5,"title":"İlk Örnek Problemin Çözümü","list":{"type":"unordered","items":["Çarpımın türevi formülü kullanılarak her iki tarafın x'e göre türevi alınır.","Türev alma işleminden sonra y'nin türevine sahip olan ifadeler bir tarafa, sahip olmayanlar diğer tarafa toplanır.","Sonuç olarak y'nin türevi (dy/dx) yalnız bırakılarak türev fonksiyonu elde edilir."]},"beginTime":773,"endTime":1006,"href":"/video/preview/3853625895084701349?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=773&ask_summarization=1"},{"index":6,"title":"İkinci Örnek Problemin Çözümü","list":{"type":"unordered","items":["İkinci örnek de kapalı fonksiyon olduğu için her iki tarafın x'e göre türevi alınır.","e üzeri x y 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3D Distance Formula: • How To Find The Distance Between 2 Points ... 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üniversite matematiği derslerinden calculus-I dersine ait \"Bileşke Fonksiyonun Türevi \" videosudur. Hazırlayan: Kemal Duran (Matematik Öğretmeni) http://www.buders.com/kadromuz.html...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3382530/eb85c7b6010d4bedd315263db26e1d57/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/oy8mCAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"19","reqid":"1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=videoid:9106820147054654643","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında bir ders anlatımıdır. Eğitmen, bileşke fonksiyonun türevi konusunu detaylı şekilde açıklamaktadır.","Video, bileşke fonksiyonun ne olduğunu hatırlatarak başlıyor ve ardından bileşke fonksiyonun türevinin nasıl alınacağını formülle açıklıyor. Eğitmen, f(g(x)) ve g(f(x)) gibi bileşke fonksiyonların türevlerini hesaplama yöntemini örneklerle gösteriyor. Özellikle f(3x-2) gibi fonksiyonların türevini alırken \"f'in türevini aldığımızı söyleyip çarpı içerisinin türevi\" kuralını uygulamalı olarak anlatıyor. Video, birkaç örnek üzerinden konuyu pekiştiriyor ve sınavlara hazırlık için önemli bilgiler sunuyor."]},"endTime":689,"title":"Bileşke Fonksiyonun Türevi Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Bileşke Fonksiyonun Tanımı","list":{"type":"unordered","items":["Bileşke fonksiyonlar f(g(x)) veya g(f(x)) biçiminde yazılır.","Bileşke fonksiyonda iki fonksiyon birleştirilir; örneğin f(x) = 2x-1 ve g(x) = 3x+2 ise f(g(x)) = 6x+3 olur.","Bileşke işleminin değişme özelliği yoktur, yani f(g(x)) ile g(f(x)) birbirine eşit çıkmayabilir."]},"beginTime":0,"endTime":123,"href":"/video/preview/9106820147054654643?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=0&ask_summarization=1"},{"index":1,"title":"Bileşke Fonksiyonun Türevi","list":{"type":"unordered","items":["Bileşke fonksiyonun türevi (f(g(x)))' = f'(g(x)) × g'(x) formülüyle hesaplanır.","Bileşke fonksiyon, f(x) yerine f(g(x)) gibi bir ifade içerdiğinde kullanılır.","Bileşke fonksiyonun türevi alırken, dış fonksiyonun türevi alınır ve iç fonksiyonun türevi ile çarpılır."]},"beginTime":123,"endTime":309,"href":"/video/preview/9106820147054654643?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=123&ask_summarization=1"},{"index":2,"title":"Örneklerle Bileşke Fonksiyon Türevi","list":{"type":"unordered","items":["f(x²) = 4x²-7x+3 fonksiyonunun türevi f'(x²) × 2x = (8x-7) × 2x = 16x²-14x olur.","f(4x+5) = x²-7x+6 fonksiyonunun türevi f'(4x+5) × 4 = (2x-7) × 4 = 8x-28 olur.","Bileşke fonksiyon türevi sayesinde f(x) yerine f(g(x)) şeklindeki fonksiyonların türevi de alınabilir."]},"beginTime":309,"endTime":572,"href":"/video/preview/9106820147054654643?parent-reqid=1773750690444596-15734497976367578984-balancer-l7leveler-kubr-yp-klg-177-BAL&text=Calculus+Corner&t=309&ask_summarization=1"},{"index":3,"title":"Bileşke Fonksiyon Türevi 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