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Parametrik va oshkormas ko‘rinishda berilgan
funksiyalarni differensiyallash
EMBED Equation.3 intervalda EMBED Equation.3 o’zgaruvchining EMBED Equation.3 va EMBED Equation.3 funksiyalari biror EMBED Equation.3 intervalda aniqlangan bo‘lib, bu intervalda EMBED Equation.3 , EMBED Equation.3 hosilalar va EMBED Equation.3 funksiyaga teskari EMBED Equation.3 funksiya mavjud bo‘lsin. Agar EMBED Equation.3 funksiya qat’iy monoton bo‘lsa, EMBED Equation.3 teskari funksiya bir qiymatli, uzluksiz va qat’iy monoton bo‘ladi. Shu sababli EMBED Equation.3 murakkab funksiya mavjud bo‘ladi. Bunda EMBED Equation.3 funksiya EMBED Equation.3 va EMBED Equation.3 tenglamalar bilan parametrik ko’rinishda ( EMBED Equation.3 parametrli) berilgan deyiladi.
EMBED Equation.3 funksiya
EMBED Equation.3
parametrik tenglamalar bilan berilgan bo‘lsin. U holda EMBED Equation.3 teskari funksiya mavjud va uning hosilasi EMBED Equation.3 . Shuningdek EMBED Equation.3 murakkab funksiya hosilasi EMBED Equation.3 bo‘ladi.
Bundan
EMBED Equation.3 yoki EMBED Equation.3 . (1)
Misol. EMBED Equation.3 funksiya uchun EMBED Equation.3 ni topamiz:
EMBED Equation.3
Agar funksiya EMBED Equation.3 ga nisbatan yechilmagan, ya’ni EMBED Equation.3 ko‘rinishda berilgan bo‘lsa, funksiya oshkormas ko’rinishda berilgan deyiladi.
Oshkor berilgan har qanday EMBED Equation.3 funksiyani oshkormas ko‘rinishda EMBED Equation.3 kabi yozish mumkin, ammo teskarisini hamma vaqt bajarib bo‘lmaydi, EMBED Equation.3 tenglamani EMBED Equation.3 ga nisbatan yechish hamma vaqt ham oson emas, ayrim hollarda esa umuman mumkin emas.
Funksiya oshkormas ko‘rinishda berilgan bo‘lsa, EMBED Equation.3 funksiya EMBED Equation.3 ning murakkab funksiyasi deb qaraladi va EMBED Equation.3 tenglikning chap va o‘ng tomoni
EMBED Equation.3 bo‘yicha differensiyalanadi, so‘ngra hosil bo’lgan tenglamadan EMBED Equation.3 topiladi.
Misol. EMBED Equation.3 funksiya uchun EMBED Equation.3 ni topamiz. Bunda tenglikning har ikkala tomonini EMBED Equation.3 bo’yicha differensiallaymiz:
EMBED Equation.3 .
Bundan
EMBED Equation.3 , EMBED Equation.3
yoki
EMBED Equation.3