logarifmik hosila. daraja-ko‘rsatkichli funksiyaning hosilasi

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1629203146.doc y ' y )' y (ln = n , 1 n n u ' u u ' u u ' u y ' y + + + = l 2 2 1 1 ÷ ÷ ø ö ç ç è æ + + + n n u ' u u ' u u ' u l 2 2 1 1 4 3 2 3 2 1 ) x ( ) x ( ) x ( + + + y ' y 3 4 2 3 1 2 + - + - + x x x 4 3 2 3 2 1 ) x ( ) x ( ) x ( + + + 3 4 2 3 1 2 + - + - + x x x 5 4 2 3 2 5 14 5 1 ) x ( ) x ( ) x x )( x ( + …

x)v(x)((ln(u(x)v(x))’=u(x)v(x)(v(x)(lnu(x))’=u(x)v(x)(v’(x)lnu(x)+v(x)( ) bo‘ladi. bundan (u(x)v(x))’=u(x)v(x)lnu(x)(v’(x)+v(x)(u(x)v(x)-1(u’(x) formula kelib chiqadi. shunday qilib, daraja-ko‘rsatkichli funksiyaning hosilasi ikkita qo‘shiluvchidan iborat: agar u(x)v(x) ko‘rsatkichli funksiya deb qaralsa birinchi qo‘shiluvchi, agar u(x)v(x) darajali funksiya deb qaralsa ikkinchi qo‘shiluvchi hosil bo‘ladi. misol. y=xx-1 funksiyaning hosilasini toping. yechish. (7.1) formulani qo‘llaymiz. y’=y((lnxx-1)’=xx-1(((x-1)lnx)’= xx-1((lnx+1- ). adabiyotlar 1. azlarov. t., mansurov. x., matematik analiz. t.: «o‘zbekiston». 1 t: 1994, 2 t . 1995 2. toshmetov o‘. matematik analiz. matematik analizga kirish. t., tdpu. 2005y. 3. hikmatov a.g‘., turdiyev t. «matematik analiz», t.1-qism.1990y. 4. sa’dullayev a. va boshqalar. matematik analiz kursi misol va masalalar to`plami. t., «o‘zbekiston». 1-q. 1993., 2-q. 1995. 5. vavilov v.v. i dr. zadachi po matematike. nachala analiza. m.nauka.,1990.-608s. 6. www.ziyonet.uz _1193313305.unknown _1193313323.unknown _1193313340.unknown _1193313421.unknown _1193313422.unknown _1193313420.unknown _1193313331.unknown _1193313314.unknown _1189274131.unknown _1193313263.unknown _1189275919.unknown _1189273875.unknown

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1629203146.doc y ' y )' y (ln = n , 1 n n u ' u u ' u u ' u y ' y + + + = l 2 2 1 1 ÷ ÷ ø ö ç ç è æ + + + n n u ' u u ' u u ' u l 2 2 1 1 4 3 2 3 2 1 ) x ( ) x ( ) x ( + + + y ' y 3 4 2 3 1 2 + - + - + x x x 4 3 2 3 2 1 ) x ( ) x ( ) x ( + + + 3 4 2 3 1 2 …

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