Murakkab funksiyaning hosilasi
Javoblar ota-onalar va o‘qituvchilar uchun.
1
y = (5 − 2x)⁸ ning hosilasini toping.
y′ = 8(5 − 2x)⁷ · (−2) = −16(5 − 2x)⁷.
2
y = e^(x²) · sin 2x ning hosilasini yozing.
y′ = 2x e^(x²) sin 2x + 2 e^(x²) cos 2x = 2e^(x²)(x sin 2x + cos 2x).
3
h(x) = (x³ − 2)⁴ ning x = 1 dagi hosilasini hisoblang.
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4
y = ln(x² + 1) ning hosilasini toping va uning ishorasini x ning ishorasi bilan bog‘lang.
y′ = 2x/(x² + 1). Maxraj doim musbat, shuning uchun y′ ning ishorasi x ning ishorasi bilan bir xil.
5
y = tg 5x ning hosilasini toping.
y′ = 5/cos²5x.