Hosilaning iqtisodga tadbiqlari

Logarifmik differensiallash
Ayrim hollarda funksiyaning hosilasini topish uchun avval berilgan funksiyani logarifmlash, so‘ngra differensiallash maqsadga muvofiq bo‘ladi. Bu jarayonga logarifmik differensiallash deyiladi.
Murakkab funksiyani hosilasi
EMBED Equation.3 va EMBED Equation.3 bo‘lsin. U holda EMBED Equation.3 funksiya erkli argumenti
EMBED Equation.3 dan va oraliq argumenti EMBED Equation.3 dan iborat murakkab funksiya bo‘ladi.
2-teorema. Agar EMBED Equation.3 funksiya EMBED Equation.3 nuqtada EMBED Equation.3 hosilaga ega bo‘lsa va EMBED Equation.3 funksiya mos EMBED Equation.3 nuqtada EMBED Equation.3 hosilaga ega bo‘lsa, u holda EMBED Equation.3 murakkab funksiya EMBED Equation.3 nuqtada differensiallanuvchi va
EMBED Equation.3
bo‘ladi.
Isboti. EMBED Equation.3 funksiya EMBED Equation.3 nuqtada differensiallanuvchi bo‘lgani uchun
EMBED Equation.3 bo‘ladi. Bundan EMBED Equation.3 .
EMBED Equation.3 funksiya EMBED Equation.3 nuqtada hosilaga ega. Shu sababli EMBED Equation.3 funksiya
EMBED Equation.3 nuqtada uzluksiz va EMBED Equation.3 da EMBED Equation.3 .
U holda
EMBED Equation.3
Bundan EMBED Equation.3 yoki
EMBED Equation.3 .
Shunday qilib, EMBED Equation.3 , ya’ni murakkab funksiyaning hosilasi berilgan funksiyaning oraliq argument bo‘yicha hosilasi bilan oraliq argumentning erkli argument bo‘yicha hosilasining ko‘paytmasiga teng.
Bu qoida oraliq argumentlar bir nechta bo‘lganda ham o‘z kuchida qoladi.
Masalan, EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 bo‘lsa, EMBED Equation.3 bo‘ladi.