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hesaplanır."]},"beginTime":898,"endTime":1038,"href":"/video/preview/6538981202598713059?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=898&ask_summarization=1"},{"index":9,"title":"Logaritmik Fonksiyonların Türevi","list":{"type":"unordered","items":["f(x) = ln(cosx + 3√2 + sinx) fonksiyonunun türevi, f'(x) = (cosx + 3√2 + sinx) / (ln(cosx + 3√2 + sinx)) olarak bulunur.","f(x) = 3ˣ fonksiyonunun türevi, f'(x) = 3ˣ × ln3 olarak hesaplanır.","g(x) = log₂x fonksiyonunun türevi, g'(x) = 1 / (x × ln2) olarak bulunur."]},"beginTime":1038,"endTime":1284,"href":"/video/preview/6538981202598713059?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=1038&ask_summarization=1"},{"index":10,"title":"Arksinüs Fonksiyonunun Türevi","list":{"type":"unordered","items":["f(x) = arksinüs(sinüs x) fonksiyonunun tersini bulmak için türev alma yöntemi kullanılır.","Arksinüs fonksiyonunun türevi, içerideki ifadenin türevi bölü kök(1 - içerideki ifadenin karesi) şeklinde hesaplanır.","Arksinüs(x²) fonksiyonunun türevi ise 2x/(1 - x⁴) olarak bulunur."]},"beginTime":1295,"endTime":1491,"href":"/video/preview/6538981202598713059?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=1295&ask_summarization=1"},{"index":11,"title":"Tanjant Doğrusu Bulma","list":{"type":"unordered","items":["Bir eğrinin belirli bir noktadaki tanjant doğrusunun eğimi, o noktadaki fonksiyonun türevine eşittir.","f(x) = eˣ + 2 + 4x³ fonksiyonunun 0,1 noktasındaki türevi 3'tür.","Eğimi 3 olan ve (0,1) noktasından geçen doğru denklemi y = 3x + 1 olarak bulunur."]},"beginTime":1491,"endTime":1630,"href":"/video/preview/6538981202598713059?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=1491&ask_summarization=1"},{"index":12,"title":"Paralel Doğrunun Üzerindeki Nokta","list":{"type":"unordered","items":["Bir eğrinin belirli bir doğrusuna paralel olan bir noktasının varlığını göstermek için, o noktadaki fonksiyonun türevinin paralel doğrunun eğimine eşit olması gerekir.","f(x) = eˣ + 2 + 4x³ fonksiyonunun türevi f'(x) = eˣ + 2 + 4x² + 4x³'tür.","f'(x) = 2 eşitliğini sağlayan bir x değeri için, intermit value teoremi kullanılarak bu noktanın varlığı gösterilir."]},"beginTime":1630,"endTime":1830,"href":"/video/preview/6538981202598713059?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=1630&ask_summarization=1"},{"index":13,"title":"İç İçe Fonksiyonların Türevi","list":{"type":"unordered","items":["f(x) = sin(sec x) fonksiyonunun türevi hesaplanırken, sec x = 1/cos x olarak tanımlanır.","Bölüm türevi formülü kullanılarak f'(x) = tan x / cos sec x bulunur.","Bu sonuç, sec x'in türevine 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formülü kullanılır.","Logaritma fonksiyonlarının türevi hesaplanırken, logaritmanın tabanı ve fonksiyonun değeri dikkate alınmalıdır."]},"beginTime":2006,"endTime":2101,"href":"/video/preview/6538981202598713059?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=2006&ask_summarization=1"},{"index":16,"title":"Teğet ve Normal Line","list":{"type":"unordered","items":["Teğet line ile normal line birbirleriyle dik kesişir ve eğimlerinin çarpımı -1'e eşittir.","Eğrinin türevi alınarak teğet line'ın eğimi (m) bulunabilir.","Normal line'ın eğimi, teğet line'ın eğiminin tersi ve işaretinin tersi olarak hesaplanır."]},"beginTime":2101,"endTime":2270,"href":"/video/preview/6538981202598713059?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=2101&ask_summarization=1"},{"index":17,"title":"Fonksiyonların Sürekliliği ve Türevlenebilirliği","list":{"type":"unordered","items":["Polinom tipteki fonksiyonlar tüm reel sayılarda süreklidir ve türevlenebilirdir.","Intermediate Value Theorem kullanılarak fonksiyonların belirli aralıklarda değerleri karşılaştırılabilir.","Fonksiyonun belirli aralıklarda değerleri karşılaştırıldığında, en az bir noktada fonksiyonun belirli bir değere eşit olduğu sonucuna varılabilir."]},"beginTime":2270,"endTime":2366,"href":"/video/preview/6538981202598713059?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=2270&ask_summarization=1"},{"index":18,"title":"Kübik Fonksiyonun Kökleri","list":{"type":"unordered","items":["Kübik fonksiyonun kökleri hesaplanarak P₁ = -3, P₂ = 8 ve P₃ = 12 olarak bulunuyor.","Fonksiyonun üç reel kökü olduğu gösteriliyor.","Türev yöntemi ile de köklerin varlığı gösterilebilir: f'(x) = 3x² - 5 = 0 denkleminin kökleri -√5/3 ve +√5/3 olup, bu noktaların görüntülerinin zıt işaretli olması üç reel kökün varlığını garanti eder."]},"beginTime":2367,"endTime":2543,"href":"/video/preview/6538981202598713059?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=2367&ask_summarization=1"},{"index":19,"title":"Süreklilik ve Türevlenebilirlik","list":{"type":"unordered","items":["Sabit c ve d değerleri için hem sürekli hem diferansiyellenebilir bir fonksiyon bulunması isteniyor.","Süreklilik için x=3 noktasındaki soldan ve sağdan limitlerin eşit olması gerekiyor: 3c+4 = 8d.","Türevlenebilirlik için x=3 noktasındaki sağ ve sol türevlerin eşit olması gerekiyor: 6d = c.","Bu denklemlerden d = -2/5 ve c = -12/5 değerleri bulunuyor."]},"beginTime":2543,"endTime":2685,"href":"/video/preview/6538981202598713059?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=2543&ask_summarization=1"},{"index":20,"title":"Dersin Kapanışı","list":{"type":"unordered","items":["Eğitmen, 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ve soldan limitler eşitse, fonksiyonun o noktada limiti vardır.","Fonksiyon değerleri ve limit değerleri farklı olabilir, limit hesaplamasında fonksiyon değerleri kullanılmaz."]},"beginTime":483,"endTime":571,"href":"/video/preview/1389943109375860163?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=483&ask_summarization=1"},{"index":5,"title":"Parametreli Fonksiyonlarda Limit","list":{"type":"unordered","items":["Parametreli parçalı fonksiyonlarda limitin olması için sağdan ve soldan limitlerin eşit olması gerekir.","Limitin olması şartıyla parametre değeri bulunabilir.","Polinom fonksiyonların her yerde limiti vardır, kritik noktaların incelenmesi gerekir."]},"beginTime":571,"endTime":728,"href":"/video/preview/1389943109375860163?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=571&ask_summarization=1"},{"index":6,"title":"Çoklu Kritik Noktada 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Her problem için çözüm mantığı detaylı olarak açıklanmakta ve doğru cevaplar verilmektedir.","Video, günlük hayattan örneklerle konuyu somutlaştırmakta ve öğrencilerin bu tür problemleri nasıl çözebileceklerini göstermektedir. Özellikle zor soruların çözümü için ayrıntılı anlatım yapılmakta ve izleyicilerin mantığını anlamaları için çeşitli yollar sunulmaktadır."]},"endTime":2275,"title":"Periyodik Durum İçeren Matematik Problemleri Çözüm Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Periyodik Durum İçeren Problemler","list":{"type":"unordered","items":["Periyodik durum içeren problemler günlük hayatta kullandığımız problemlerdir.","Miray TYT soru bankasının 244-248 sayfalarındaki periyodik durum içeren problemler çözülecektir.","Gün sorularında periyodumuz yedi gündür, yani günler yedi günde bir tekrar eder."]},"beginTime":4,"endTime":66,"href":"/video/preview/7475136019834126087?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=4&ask_summarization=1"},{"index":1,"title":"Gün Problemleri Örnekleri","list":{"type":"unordered","items":["Bugün günlerden çarşamba ise 137 gün önce hangi gün olur sorusunda, 137'yi 7'ye bölerek 19 hafta ve 4 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saat 4:30'a ulaşılır.","Sorunun doğru cevabı B şıkkıdır."]},"beginTime":922,"endTime":969,"href":"/video/preview/7475136019834126087?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=922&ask_summarization=1"},{"index":7,"title":"Harf Dizisi Problemi","list":{"type":"unordered","items":["Verilen harf dizisinde baştan 2020. harf nedir soruluyor.","Dizide \"kurtçu\" kelimesi 6 kez tekrar ediyor.","2020'yi 6'ya böldüğümüzde kalan 4 olduğu için 4. harf olan T cevabıdır."]},"beginTime":969,"endTime":1064,"href":"/video/preview/7475136019834126087?parent-reqid=1769135893263708-2349168039756629146-balancer-l7leveler-kubr-yp-vla-182-BAL&text=Ill+Mat+-+Topic&t=969&ask_summarization=1"},{"index":8,"title":"Şehir Problemi","list":{"type":"unordered","items":["Her nokta bir şehri göstermek üzere, A şehrinde bulunan Forrest Gump ok yönünde koşmaya başlıyor.","Forrest Gump durduğunda 1517 şehir geçtiğini söylemiştir.","Forrest Gump hangi 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