Question

помогите, пожалуйста. Очень срочно ​

Answer 1

Ответ:

1

1.

$f'(x) = - 40 {x}^{7}$

2

$f'(x) = \frac{1}{12} \times ( - 12) {x}^{ - 13} = - \frac{1}{ {x}^{13} }$

3

$f'(x) = 6 \times ( - {x}^{ - 2} ) = - \frac{6}{ {x}^{2} }$

4

$f'(x) = 9 \times \times \frac{1}{2} {x}^{ - \frac{1}{2} } = \frac{9}{2 \sqrt{x} }$

5

$f'(x) = 0$

6

$f'(x) = 44 {x}^{10} - 9 {x}^{8} + 18 {x}^{5} + 4 {x}^{3} - 12x + 1$

7

$f'(x) = - \frac{1}{ { \cos}^{2} x} - \frac{1}{ { \sin}^{2} } + 2 \sin(x)$

8

$f'(x) = \cos(x) + 14 {x}^{13}$

9

$f'(x) = - \frac{1}{ { \sin }^{2}x } - 12 \times ( - {x}^{ - 2} ) - 7 = \\ = - \frac{1}{ { \sin}^{2} x} + \frac{12}{ {x}^{2} } - 7$

10

$f'(x) = ((5 + 4x) {x}^{7} )' = (5 {x}^{7} + 4 {x}^{8} ) '= \\ = 35 {x}^{6} + 32 {x}^{7}$

11

$f'(x) = (3x - 18)'(1 + 5x) + (1 + 5x)'(3x - 18) = \\ = 3(1 + 5x) + 5(3x - 18) = \\ = 3 + 15x + 15x - 90 = 30x - 87$

12

$f'(x) = ( - 5x)'( \sin(x) + x) + (x + \sin(x) ) '\times ( - 5x) = \\ = - 5(x + \sin(x) ) + (1 + \cos(x) ) \times ( - 5x) = \\ = - 5(x + \sin(x) + x+ x\cos(x) ) = \\ = - 5( \sin(x) + x\cos(x) + 2x)$

13

$f'(x) = \frac{(2x - 3)'(2x + 5) - (2x + 5)'(2x - 3)}{ {(2x + 5)}^{2} } = \\ = \frac{2(2x + 5) - 2(2x - 3)}{ {(2x + 5)}^{2} } = \frac{4x + 10 - 4x + 6}{ {(2x + 5)}^{2} } = \\ = \frac{16}{ {(2x + 5)}^{2} }$

14

$f'(x) = \frac{( {x}^{7} - 2 {x}^{6} + x)' \times \cos(x) - (\cos(x))' \times ( {x}^{7} - 2 {x}^{6} + x) }{ { \cos }^{2}x } = \\ = \frac{(7 {x}^{6} - 12 {x}^{5} + 1) \cos(x) - \sin(x) \times ( {x}^{7} - 2 {x}^{6} + x) }{ { \cos }^{2}x }$

15

$f'(x) = ( \frac{5 {x}^{8} + 3 }{ \sqrt{x} } ) '= ( \frac{5 {x}^{8} }{ \sqrt{x} } + \frac{3}{ \sqrt{x} } )' = \\ = (5 {x}^{ \frac{7}{2} } + 3 {x}^{ - \frac{1}{2} } )' = 5 \times \frac{7} {2} {x}^{ \frac{5}{2} } - 3 \times \frac{1}{2} {x}^{ - \frac{3}{2} } = \\ = \frac{35}{2} {x}^{2} \sqrt{x} - \frac{3}{2x \sqrt{x} }$

16

$f-(x) = 16 {(2 - 10x)}^{15} \times (2 - 10x)' = \\ = 16 {(2 - 10x)}^{15} \times ( - 10) = \\ = - 160 {(2 - 10x)}^{15}$

17

$f'(x) = \frac{1}{2} {( {x}^{17} - 9 {x}^{3} + 1.2) }^{ - \frac{1}{2} } \times ( {x}^{17} - 9 {x}^{3} + 1.2)' = \\ = \frac{17 {x}^{16} - 27 {x}^{2} }{2 \sqrt{ {x}^{17} - 9 {x}^{3} + 1.2} }$

18

$f'(x) = ( - {tg}^{ - 1} x) '= - ( - {tg}^{ - 2} x) \times (tgx) '= \\ = \frac{1}{ {tg}^{2}x } \times \frac{1}{ { \cos}^{2} x} = \frac{ { \cos }^{2}x }{ { \sin}^{2} x } \times \frac{1}{ { \cos }^{2}x } = \frac{1}{ { \sin}^{2} x}$

19

$f'(x) = - \frac{14}{ { \sin }^{2} (14x)}$

20

$f'(x) = 11 \cos(11x + \frac{\pi}{3} )$

21

$f'(x) = 4 \cos(x) - ( {(x - 5 {x}^{8} )}^{ - 1} ) '= \\ = 4 \cos(x) - {(x - 5 {x}^{8}) }^{ - 2} \times (1 - 40 {x}^{7} )' = \\ = 4 \cos(x) - \frac{1 - 40 {x}^{7} }{ {(x - 5 {x}^{8}) }^{2} }$

2

1

$f'(x) = 36 {x}^{3} - 6x + 0 = 36 {x}^{6} - 6x \\ f'(5) = 36 \times 125 - 30 = 4470\\ f'( - \frac{ 1}{3} ) = - \frac{36}{27} + 2 = - \frac{4}{3} + 2 = \\ = \frac{ - 4 + 6}{3} = \frac{2}{3}$