Question

50 баллов. Найти производные:(см.фото)

Answer 1

Ответ:

1.

$y' = 3 {x}^{2} - 6x - \frac{1}{6} \times ( - 6) {x}^{ - 7} = \\ = 3 {x}^{2} - 6x + \frac{1}{ {x}^{7} }$

2.

$y' = \frac{(5 {x}^{2} - 3x)'(3x - 8) - (3x - 8)'(5 {x}^{2} - 3x) }{ {(3x - 8)}^{2} } = \\ = \frac{(10x - 3)(3x - 8) - 3(5 {x}^{2} - 3x)}{ {(3x - 8)}^{2} } = \\ = \frac{30 {x}^{2} - 80x - 9x + 24 - 15 {x}^{2} + 9x }{ {(3x - 8)}^{2} } = \\ = \frac{15 {x}^{2} - 80x + 24 }{ {(3x - 8)}^{2} }$

3.

$y' = (3 {x}^{2} )' \times 2 \sin(x) + (2 \sin(x)) ' \times 3 {x}^{2} = \\ = 6x \times 2 \sin(x) + 2 \cos(x) \times 3 {x}^{2} = \\ = 12x \sin(x) + 6 {x}^{2} \cos(x)$