Hosilaning iqtisodga tadbiqlari

Differensiallash qoidalari va hosilalar jadvali
Keltirib chiqarilgan differensiallash qoidalarini va asosiy elementar funksiyalarning hosilalari formulalarini jadval ko‘rinishida yozamiz.
Amalda ko’pincha murakkab funksiyalarning hosilalarini topishga to‘g‘ri keladi. Shu sababli quyida keltiriladigan formulalarda EMBED Equation.3 argument EMBED Equation.3 oraliq
argumentga almashtiriladi.
Differensiallash qoidalari:
1. EMBED Equation.3 EMBED Equation.3 differensiallanuvchi funksiyalar;
2. EMBED Equation.3 xususan EMBED Equation.3 EMBED Equation.3 o‘zgarmas son;
3. EMBED Equation.3 xususan EMBED Equation.3
4. EMBED Equation.3 , agar EMBED Equation.3 va EMBED Equation.3 ;
5. EMBED Equation.3 , agar EMBED Equation.3 va EMBED Equation.3 .
Asosiy elementar funksiyalarning hosilalar jadvali:
1. EMBED Equation.3
2. EMBED Equation.3 xususan EMBED Equation.3 EMBED Equation.3
3. EMBED Equation.3 xususan EMBED Equation.3
4. EMBED Equation.3 xususan EMBED Equation.3
5. EMBED Equation.3 6. EMBED Equation.3
7. EMBED Equation.3 8. EMBED Equation.3
9. EMBED Equation.3 10. EMBED Equation.3
11. EMBED Equation.3 12. EMBED Equation.3
13. EMBED Equation.3 14. EMBED Equation.3
15. EMBED Equation.3 16. EMBED Equation.3 EMBED Equation.3
Keltirilgan diferensiallash qoidalari va asosiy elementar funksiyalarning hosilalar jadvali bir o‘zgaruvchi funksiyasi differensial hisobining asosini tashkil qiladi, ya’ni ularni bilgan holda qiyinchilik darajasi qanday bo‘lishidan qat’iy nazar har qanday elementar funksiyaning hosilasini topish mumkin. Bunda yana elementar funksiya hosil bo‘ladi. Shunday qilib, differensiallash jarayonida
elementar funksiyalar sinfidan tashqariga chiqilmaydi.
Misol. EMBED Equation.3 funksiyaning hosilasini topamiz:
EMBED Equation.3 EMBED Equation.3 EMBED Equation.3
EMBED Equation.3 EMBED Equation.3
Hosilani topishda differensiallashning 1,2 qoidalari va 3,4,9 formulalaridan
foydalanildi.