Trigonometrik funksiyalar hosilasi. Teskari trigonometrik funksiyaning hosilasi

Trigonometrik funksiyalar hosilasi.Teskari trigonometrik funksiyaning hosilasi. Reja: 1.Trigonometrik funksiyalar hosilasi. 2.Teskari trigonometrik funksiyaning hosilasi. Тrigonometrik funksiyalarni hosilalari 1) (sinx)' = cosx 2) (cosx)' = - sinx 1 3) (tgx)'= cos2x 1 4) (ctg x)' = - sin 2x Isbot. Shuningdek, Ixtiyoriy, uchun Isbot. (2) formulani tengliklarga va murakkab funksiyani differensiallash qoidalariga asoslanib isbotlaymiz. (3) va (4) formulalarni esa bo'linmaning hosilasini toppish qoidasi va sinus funksiya hosilalarini toppish formulalaridan foydalanib isbotlaymiz. 1 Logarifmik funksiyani hosilasi (logax)' = x ln x x Кo'rsatkichli funksiyani hosilasi (ex)' = ех; Теskari trigonometric funksiyalarni hosilalari. 1 1 (arcsinx)' = ; (arctgx)' = - √1-x2 1+x 2 1 1 (arccosx)' = - ; (arcctgx)' = √1-x2 1+x 2 1-misol: у=(х3-1) (3х+5) ni hosilasini toping. Yechish: у= 3х4-3х+5х3-5 = 3х4+5х3-3х-5 У'= (3х4-3х+5х3-5)' = (3х4)'+(5х3)'-(3х)'-(5)'= 3(х4)'-(3х)'+5(х3)'-(5)' = 12x3+15x2-3; Х2 2-misol. у= ni hosilasini toping. 1+х x2 ( x2)'.(1+x)-(1+x)'.x2 2x(1+x)-x2 2x+2x2-x2 y'= ( ) ' = = = = 1+x (1+x)2 (1+x)2 (1+x)2 x2+2x x(x+2) = = (1+x)2 (1+x)2 3-misol. у= 5 cos 6x ni hosilasini toping. y'= (5cos6x)' = 5(cos6x)' = 5 (-sin6x) (6x)' = -5 sin6x.6 = -30 sin6x 4-misol. y= ecosx ni hosilasini toping. у' =( ecosx)' = ecosx(cosx)' = - ecosx.sinx 5-misol .y= arcsin 10 x hosilasini toping. 1 10 y' = (arcsin 10 x)'= .(10x)'= √1- (10x)2 √1- 100x2 Nazorat savollari. 1.Trigonometrik funksiyalar hosilasini topish formulasini yozing? 2.Teskari trigonometrik funksiyaning hosilasini Missollar. Funksiyalarning hosilasini toping: 1. 2. 3. 4. 5. 6. Funksiyalar differensialini toping: 1. 2. 3. 4. Quyidagilarni taqribiy hisoblang: 1. 2. 3. 4. Tayanch so'zlar. Hosila, darajali funksiya, logarifm, natural logarifm, ko'rsatkichli funksiya, trigonometric funksiya, teskari funksiya. Adabiyotlar. 1.Algebra va analiz asoslari:Akad.litsiy va kasb-hunar kollejlari uchun darslik R. H. Vafayev, J. H. Husanov, K. H. Fa. yziyev 1-qism 269-274 bet. 2.Algebra va matematik analiz asoslari. Akad. Litseylar uchun darslik A.U.Abduhamedov, H. A. Nasimov, U. M. Nosirov, J. H. Husanov, H. A. Nasimov. 2- qism ...