Question

(50)производные , помогите пж​ все отдельно

Answer 1

Ответ:

1.

$y = 3 {x}^{3} + 2x - 1 \\ y' = 3 \times 3 {x}^{2} + 2 - 0 = \\ = 9 {x}^{2} + 2$

2.

$y = (2x + 1)(3x + 1)$

$y' = (2x + 1)'(3x + 1) + (3x + 1)'(2x + 1) = \\ = 2(3x + 1) + 3(2x + 1) = 6x + 2 + 6x + 3 = \\ = 12x + 5$

3.

$y = \frac{2x}{x + 1}$

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