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Peki Fatih, neden bir mezarın peşine düştü? Eyüp Sultan’ın kabri nasıl bulundu? 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takip edenlerden ricam eski nesil yeni nesil yok.her şeyi çözeceksiniz. bu kanalda sizi kandırmadan gerçekten başarılı olmanız için çalışıyorum. bu sınavda çıkmaz, ösym tarzı değil, bu...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3794342/c200ec29ab6a42c7f30868e77061e5ec/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/RsMdWwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"17","reqid":"1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL&text=videoid:16806113494058355461","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeni tarafından sunulan türev konusunu anlatan eğitim içeriğidir. Öğretmen, ÖSYM'nin yasaklarından dolayı önceki videoların silinmesi üzerine türev konusunu tekrar anlatmaktadır.","Video, türev konusunun temel kavramlarını ve türevin limit tanımını detaylı şekilde ele almaktadır. İlk bölümde ortalama değişim oranı kavramı anlatılmakta, ardından türevin limit tanımı (f'(x) = limit h sıfıra giderken (f(x+h) - f(x)) / h) formülüyle açıklanmaktadır. Video yaklaşık 20 dakika sürmekte ve ikinci videoda türev alma kurallarının gösterileceği belirtilmektedir.","Videoda türevin farklı gösterim biçimleri (f'(x), dy/dx, d/dx), sabit sayıların türevinin sıfır olduğu ve farklı fonksiyonlarda türevin nasıl bulunacağı adım adım örneklerle gösterilmektedir. Ayrıca uzun yoldan türev hesaplama yöntemleri de içermektedir."]},"endTime":1423,"title":"Türev Konusu Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Türev Konusunun Önemi","list":{"type":"unordered","items":["Türev konusu ÖSYM'nin yasaklarından dolayı tekrar anlatılacak ve çıkmış soruların benzerleri veya karşınıza çıkabilecek sorular tekrar edilecek.","Türeve başlarken ortalama değişim oranından bahsetmek gerekir çünkü bu, türevin limit tanımından yararlanarak türeve geçiş için temeldir.","MEB kitabında ortalama değişim oranı ayrıntılı şekilde bahsedilmiş ve ÖSYM bununla ilgili güzel sorular sorabilir."]},"beginTime":0,"endTime":58,"href":"/video/preview/16806113494058355461?parent-reqid=1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL&text=Ey%C3%BCp+Do%C4%9Fan&t=0&ask_summarization=1"},{"index":1,"title":"Ortalama Değişim Oranı","list":{"type":"unordered","items":["Ortalama değişim hızı, f(b) - f(a) / (b - a) formülüyle bulunur ve doğrunun eğimini hesaplamak için kullanılır.","Örneğin, f(x) = x² + 4 fonksiyonunun 1 ile 4 aralığında ortalama değişim oranı 5'tir.","f(x) = 2x + 4 fonksiyonunun 2 ile 4 aralığında ortalama değişim hızı 2'dir ve bu doğrunun eğimi de 2'dir."]},"beginTime":58,"endTime":188,"href":"/video/preview/16806113494058355461?parent-reqid=1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL&text=Ey%C3%BCp+Do%C4%9Fan&t=58&ask_summarization=1"},{"index":2,"title":"Anlık Değişim Oranı ve Türev","list":{"type":"unordered","items":["Eğrilerin değişim hızını bulurken anlık değişim oranından yararlanılır ve bu aynı zamanda o anda eğriye çizilen teğetin eğimidir.","Anlık değişim oranı, teğetin eğimi ve türev aynı şeydir ve o noktadaki türevi verir.","Türevin limit tanımı, h değeri sıfıra yaklaştığında ortalama değişim oranının anlık değişime dönüşmesiyle elde edilir ve bu formül türevin çıkış noktasıdır."]},"beginTime":188,"endTime":333,"href":"/video/preview/16806113494058355461?parent-reqid=1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL&text=Ey%C3%BCp+Do%C4%9Fan&t=188&ask_summarization=1"},{"index":3,"title":"Türevin Limit Tanımı","list":{"type":"unordered","items":["Bir x üzeri n fonksiyonunun türevi n çarpı x üzeri n eksi bir olarak hesaplanır.","Türevin limit tanımı: limit h sıfıra giderken (f(x+h) - f(x)) / (h) şeklindedir.","Bu formül, doğrunun eğimi formülüne benzer şekilde y2-y1/x2-x1 şeklinde ifade edilir."]},"beginTime":342,"endTime":404,"href":"/video/preview/16806113494058355461?parent-reqid=1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL&text=Ey%C3%BCp+Do%C4%9Fan&t=342&ask_summarization=1"},{"index":4,"title":"Türevin Limit Tanımıyla Hesaplanması","list":{"type":"unordered","items":["f(x) = x² fonksiyonunun türevi limit tanımıyla hesaplandığında, limit h sıfıra giderken (x+h)² - x² / h = 2x olarak bulunur.","Türevin limit tanımı formülü ezbere bilinmelidir.","Türevin farklı gösterim şekilleri: f'(x), df(x) / dx veya (f(x+h) - f(x)) / h'dir."]},"beginTime":404,"endTime":545,"href":"/video/preview/16806113494058355461?parent-reqid=1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL&text=Ey%C3%BCp+Do%C4%9Fan&t=404&ask_summarization=1"},{"index":5,"title":"Türevin Diğer Formülleri","list":{"type":"unordered","items":["Türevin başka bir formülü: limit h sıfıra giderken (f(x) - f(a)) / (x-a) şeklindedir.","x³ fonksiyonunun türevi limit tanımıyla hesaplandığında, limit h sıfıra giderken (x+h)³ - x³ / h = 3x² olarak bulunur.","Sabit sayıların türevi sıfırdır, örneğin 5x⁰ = 5'in türevi 0'dır."]},"beginTime":545,"endTime":784,"href":"/video/preview/16806113494058355461?parent-reqid=1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL&text=Ey%C3%BCp+Do%C4%9Fan&t=545&ask_summarization=1"},{"index":6,"title":"Türevin Limit Tanımından Çözüm","list":{"type":"unordered","items":["Öğretmenlerin L'Hospital kuralı yerine türevin limit tanımından çözüm önermesi gerektiği vurgulanıyor.","Sorularda yeni formüller üretmek yerine, öğrendiğimiz formülleri uyarlamak daha etkili bir yöntemdir.","Türevin limit tanımından çözüm yaparken, h yerine -h/3 gibi değerler yazarak formüle benzetme yapılabilir."]},"beginTime":792,"endTime":929,"href":"/video/preview/16806113494058355461?parent-reqid=1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL&text=Ey%C3%BCp+Do%C4%9Fan&t=792&ask_summarization=1"},{"index":7,"title":"Türevin Limit Tanımından Örnek Sorular","list":{"type":"unordered","items":["Türevin limit tanımından çözüm yaparken, f(x) yerine f(x-3h) gibi ifadeler ekleyerek formüle uygun hale getirilebilir.","Limit hesaplamalarında, h yerine -h/3 veya h/2 gibi değerler yazarak formüle benzetme yapılabilir.","Türevin limit tanımından çözüm yaparken, limit hesaplamalarında dikkatli olmak ve formülün tam olarak nasıl uygulanacağını anlamak önemlidir."]},"beginTime":929,"endTime":1144,"href":"/video/preview/16806113494058355461?parent-reqid=1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL&text=Ey%C3%BCp+Do%C4%9Fan&t=929&ask_summarization=1"},{"index":8,"title":"Türevin Limit Tanımından Zor Sorular","list":{"type":"unordered","items":["Türevin limit tanımından çözüm yaparken, f(x+y) - f(x) = (x³+2x+5)/y şeklinde verilen denklemlerde, limit y sıfıra giderken alınabilir.","Türevin limit tanımından çözüm yaparken, limit hesaplamalarında y yerine sabit bir değer yazılabilir.","Türevin limit tanımından çözüm yaparken, limit hesaplamalarında verilen bilgilere göre f'(x) formülü elde edilebilir."]},"beginTime":1144,"endTime":1261,"href":"/video/preview/16806113494058355461?parent-reqid=1765126165928798-11399622217865898391-balancer-l7leveler-kubr-yp-klg-58-BAL&text=Ey%C3%BCp+Do%C4%9Fan&t=1144&ask_summarization=1"},{"index":9,"title":"Türevin Limit Tanımından Sınav 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