Question

Найдите производные:
, помогите пожалуйста, ​

Answer 1

Ответ:

1.

----------------------------------------

$1)y' = 12 {x}^{3} - 21 {x}^{2} + 4x$

$2)y'= \frac{1}{2} {x}^{ - \frac{1}{2} } - {x}^{ - 2} = \frac{1}{2 \sqrt{x} } - \frac{1}{ {x}^{2} }$

$3)y' = 2 \cos(x)$

$4)y' = \frac{5}{ { \cos(x) }^{2} }$

$5)y' = 6 {x}^{2} - 9 \cos(3x)$

$6)y' = 3 {(3 - 4x)}^{2} \times ( - 4) = - 12 {(3 - 4x)}^{2}$

$7)y' = 2(1 - {x}^{2} ) - 2x(2x - 3) = 2 - 2 {x}^{2} - 4 {x}^{2} + 6x = - 6 {x}^{2} + 6x + 2$

____________________________

2.

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

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

$3)y' = - \frac{1}{ { \sin(4x - \frac{\pi}{3} ) }^{2} } \times 4 = \frac{ - 4}{ { \sin(4x - \frac{\pi}{3} ) }^{2} }$

$4)y' = 2 \cos(x) \times ( - \sin(x) ) = - \sin(2x)$

$5)y' = 1 \times \sin(x) + x\times \cos(x) = \sin(x) + x \cos(x)$