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lizali2
@lizali2
July 2022
1
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Report
НАПИШИТЕ ПОДРОБНО ПРОИЗВОДНУЮ ПЕРВОГО И ВТОРОГО ПОРЯДКА ДЛЯ ФУНКЦИИ
y=∛(x(x-6)^2
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sedinalana
Verified answer
Y=∛(x³-12x²+36x)
y`=(3x²-24x+36)/3∛(x³-12x²+36x)²=(x²-8x+12)/∛[x²(x-6)²]=
=(x-2)(x-6)/∛[x²(x-6)²]=(x-2)∛(x-6)/∛x²
y``=[(∛(x-6)+(x-2)/3∛(x-6)²)*∛x²-4x(x-2)∛(x-6)/3∛x]/∛x^4=
=[∛x²(x-6)+(x-2)∛x²/3∛(x-6)²-4∛x²(x-2)(x-6)/3]/∛x^4=
=[3(x-6)*∛x²+(x-2)∛x²-4∛x²(x-2)(x-6)]/3∛x^4(x-6)²=
=∛x²(3x-18+x-2-4x²+32x-48)/3∛x^4(x-6)²=(-4x²+36x-68)/3∛x^4(x-6)²
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Report "НАПИШИТЕ ПОДРОБНО ПРОИЗВОДНУЮ ПЕРВОГО И ВТОРОГО ПОРЯДКА ДЛЯ ФУНКЦИИ y=∛(x(x-6)^2..."
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Answers & Comments
Verified answer
Y=∛(x³-12x²+36x)y`=(3x²-24x+36)/3∛(x³-12x²+36x)²=(x²-8x+12)/∛[x²(x-6)²]=
=(x-2)(x-6)/∛[x²(x-6)²]=(x-2)∛(x-6)/∛x²
y``=[(∛(x-6)+(x-2)/3∛(x-6)²)*∛x²-4x(x-2)∛(x-6)/3∛x]/∛x^4=
=[∛x²(x-6)+(x-2)∛x²/3∛(x-6)²-4∛x²(x-2)(x-6)/3]/∛x^4=
=[3(x-6)*∛x²+(x-2)∛x²-4∛x²(x-2)(x-6)]/3∛x^4(x-6)²=
=∛x²(3x-18+x-2-4x²+32x-48)/3∛x^4(x-6)²=(-4x²+36x-68)/3∛x^4(x-6)²