Hosilani hisoblash qoidalari
Javoblar ota-onalar va o‘qituvchilar uchun.
1
f(x) = x⁴ − 6x² + 3x − 8 ning hosilasini toping va f′(−2) ni hisoblang.
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2
y = (x³ + 2) cos x ning hosilasini yozing.
y′ = 3x² cos x − (x³ + 2) sin x.
3
y = ln x / x (x > 0) ning hosilasini toping va x = e da hosila nolga tengligini ko‘rsating.
y′ = (1/x · x − ln x · 1)/x² = (1 − ln x)/x². x = e da ln e = 1, y′ = 0.
4
y = 3eˣ − 2 cos x + 5/x ning hosilasini toping.
y′ = 3eˣ + 2 sin x − 5/x².
5
y = x − 2 sin x funksiyaning hosilasi [0; 2π] kesmaning qaysi nuqtalarida nolga aylanadi?
y′ = 1 − 2 cos x. y′ = 0 ⇔ cos x = 1/2 ⇔ x = π/3 yoki x = 5π/3.