7-bob. Differensial hisob

Logarifmik funksiyaning hosilasi:
funksiyani hosilasi
ko’rinishida bo’ladi.
Parametrik ko’rinishida berilgan funksiyaning hosilasi. Agar funksiya parametrik ko’rinishda va berilgan bo’lsa, u holda uning hosilasi

ko’rinishida bo’ladi.
Agar y ga nisbatan yechilmagan tenglama y ni x ning bir qiymatli funksiyasi sifatida aniqlasa, u holda y o’zgaruvchi x ning oshkormas funksiyasi deyiladi. Bu oshkormas funksiyadan hosilani topish uchun y ni x ning funksiyasi deb, tenglamaning ikki tomonini x bo’yicha differensiallash kerak. Hosil bo’lgan tenglamadan izlangan ni topamiz. ni topish uchun tenglamani x bo’yicha ikki marta differensiallash kerak va hokazo.
Misol: (e^xsin 2x)= (e^x) sin 2x + e^x (sin 2x )= e^xsin 2x + e^xcos 2x(2x)=
= (sin 2x +2 cos 2x) e^x ,
.

Quyidagi funksiyalarning hosilalari topilsin.
7.73. 1) 2)
3) Funksiyaning hosilasini toping.
a) ; b) ;
v) ; g) .
7.74. 1) 2)
7.75. 1) 2)
7.76. 1) 2) 3)
7.77. 7.78.
7.79. 7.80.
7.81. 7.82.
7.83. 1) 2)
3) . funksiyaga teskari bo’lgan funksiya uchun ni toping.
4) Hosilani tekshiring. a) ; b) .
Quyidagi tenglamalardan topilsin.
7.84. 1) 2) 3)
4) . oshkormas funksiya uchun ni toping.
7.85. 1) 2)
Quyidagi funksiyalarning differensiallari topilsin:
7.86. 1) 2)
3) berilgan bo’lsa, ni toping.
7.87. 1) 2)
7.88. 1) 2)
7.89 funksiyani nuqtadagi hosilasini toping.
7.90. funksiyaning ixtiyoriy x nuqtasi uchun differensialini hisoblang.
7.91 7.92
7.93 7.94
7.95 7.96
7.97 7.98
7.99 7.100
7.101 7.102
7.103 7.104
7.105
7.106 6.107
7.108 6.109 berilgan . ni toping.
7.110 berilgan . ni toping.
7.111 berilgan . ni toping.
7.112 berilgan . ni toping.
7.113 berilgan . ni toping.
7.114 berilgan . ni toping.
7.115 berilgan . ni toping.
7.116 7.117
7.118 7.119
7.120