Найти производную *100 БАЛЛОВ* 1) f(x)=(4x+1)(9-3x) 2) f(x)=(3x^2+7)*3,6x^3. Created by N1cel. algebra-ru

Найти производную *100 БАЛЛОВ* 1) f(x)=(4x+1)(9-3x) 2) f(x)=(3x^2+7)*3,6x^3...

sobakazabiyaka

Воспользуемся свойствами производной:

( C•u )' = C•(u)'

( u + v )' = u' + v'

( u • v )' = u'•v + u•v'

1) f'(x) = ( (4x + 1)(9 - 3x) )' = (4x + 1)'•(9 - 3x) + (4x + 1)•(9 - 3x)' = 4•(9 - 3x) + (-3)•(4x + 1) = 36 - 12x - 12x - 3 = 33 - 24x

2) f'(x) = ( (3x² + 7)•3,6x³ )' = (3x² + 7)'•3,6x³ + (3x² + 7)•(3,6x³)' = 6x•3,6x³ + (3x² + 7)•10,8x² = 21,6x⁴ + 32,4x⁴ + 75,6x² = 54x⁴ + 75,6x²

3 votes Thanks 3

Mihail001192

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$1)f(x)=(4x+1)(9-3x)\\f'(x)=(4x+1)'(9-3x)+(4x+1)(9-3x)'=4(9-3x)-3(4x+1)=36-\\-12x-12x-3=33-24x=-24x+33\\ \\ 2) f(x)=(3x^2+7)*3,6x^3\\ f(x)'=(3x^2+7)'(3,6x^3)+(3x^2+7)(3,6x^3)'=6x(3,6x^3)+10,8x^2(3x^2+7)=\\ =21,6x^4+32,4x^4+75,6x^2=54x^4+75,6x^2$

1 votes Thanks 4

Answers & Comments

Воспользуемся свойствами производной:

( C•u )' = C•(u)'

( u + v )' = u' + v'

( u • v )' = u'•v + u•v'

1) f'(x) = ( (4x + 1)(9 - 3x) )' = (4x + 1)'•(9 - 3x) + (4x + 1)•(9 - 3x)' = 4•(9 - 3x) + (-3)•(4x + 1) = 36 - 12x - 12x - 3 = 33 - 24x

2) f'(x) = ( (3x² + 7)•3,6x³ )' = (3x² + 7)'•3,6x³ + (3x² + 7)•(3,6x³)' = 6x•3,6x³ + (3x² + 7)•10,8x² = 21,6x⁴ + 32,4x⁴ + 75,6x² = 54x⁴ + 75,6x²

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