Question

Нужно сделать до завтра пожалуйста помогите
Тренажер "знайди похідну "(найти производную)
фото прекрепила​​

Answer 1

Ответ:

1

$(7) '= 0$

2

$( \frac{x}{5} ) '= \frac{1}{5}$

3

$( {x}^{3} ) '= 3 {x}^{2}$

4

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

5

$((6x - 5) {}^{3} )' = 3 {(6x - 5)}^{2} \times (6x - 5) '= \\ = 3 {(6x - 5)}^{2} \times 6 = 18 {(6x - 5)}^{2}$

6

$(4(5 - 6x) {}^{3} )' = 4 \times 3 {(5 - 6x)}^{2} \times (5 - 6x) '= \\ = 12 {(5x - 6x)}^{2} \times ( - 6) = - 72 {(5 - 6x)}^{2}$

7

$( \sqrt[4]{ {x}^{3} } )' = ( {x}^{ \frac{3}{4} })' = \frac{3}{4} {x}^{ - \frac{1}{4} } = \frac{3}{4 \sqrt[4]{x} }$

8

$( \sqrt[3]{(7 - 3x) {}^{2} } )' = ( {(7 - 3x)}^{ \frac{2}{3} } ) '= \\ = \frac{2}{3} {(7 - 3x)}^{ - \frac{1}{3} } \times (7 - 3x) '= \frac{2}{3 \sqrt[3]{7 - 3x} } \times ( - 3) = \\ = - \frac{2}{ \sqrt[3]{7 - 3x} }$

9

$( \frac{1}{ {x}^{4} } ) '= ( {x}^{ - 4} )' = - 4 {x}^{ - 5} = - \frac{4}{ {x}^{5} }$

10

$( - \frac{4}{ {x}^{5} } ) '= ( - 4 {x}^{ - 5} )' = - 4 \times ( - 5) \times {x}^{ - 6} = \frac{20}{ {x}^{6} }$

11

$( \frac{2}{(7 - 2x) {}^{2} } )' = (2 {(7 - 2x)}^{ - 2} ) '= \\ = 2 \times ( - 2) {(7 - 2x)}^{ - 3} \times (7 - 2x) '= \\ = - \frac{4}{ {(7 - 2x) {}^{3} }^{} } \times ( - 2) = \frac{8}{ {(7 - 2x)}^{3} }$

12

$( \frac{1}{ \sqrt[5]{ {x}^{4} } } ) '= ( {x}^{ - \frac{4}{5} } ) '= - \frac{4}{5} {x}^{ - \frac{9}{5} } = - \frac{4}{5x \sqrt[5]{ {x}^{4} } }$

13

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

14

$( \frac{1}{ \sqrt{7 - 4x} } )' = ( {(7 - 4x)}^{ - \frac{1}{2} } ) '= \\ = - \frac{1}{2} {(7 - 4x)}^{ - \frac{3}{2} } \times ( - 4) = \frac{2}{ \sqrt{ {(7 - 4x)}^{3} } }$

15

$( \sin(4x)) '= \cos(4x) \times (4x) '= 4 \cos(4x)$

16

$( \sin(3x - \frac{\pi}{6} ) ) '= 3 \cos(3x - \frac{ \pi}{6} )$

17

$(3 \cos(3x)) '= - 3 \sin(3x) \times 3 = - 9 \sin(3x)$

18

$(2 \cos( \frac{\pi}{3} + 2x)) ' = - 4 \sin( \frac{\pi}{3} + 2x )$

19

$( \cos {}^{2} (3x + \frac{\pi}{6} )) '= \\ = 2 \cos(3x + \frac{\pi}{6} ) \times ( \cos(3x + \frac{\pi}{6} ) ) '\times (3x + \frac{\pi}{6} )' = \\ = 2 \cos(3x + \frac{\pi}{6} ) \times ( - \sin(3x + \frac{\pi}{6} ) ) \times 3 = \\ = - 3 \sin(6x + \frac{\pi}{3} )$

20

$(5 \sin {}^{ - 2} (2x - \frac{ \pi}{3} ) )' = - 10 \sin {}^{ - 3} (2x - \frac{\pi}{3} ) \times \cos(2x - \frac{\pi}{3} ) \times 2 = \\ = - \frac{20 \cos(2x - \frac{\pi}{3} ) }{ \sin {}^{3} (2x - \frac{\pi}{3} ) }$

21

$(3 {e}^{ - x} ) '= - 3 {e}^{ - x}$

22

$(5 \times {3}^{5x + 1} ) '= 5 ln(3) \times {3}^{5x + 1} \times 5 = \\ = 25 ln(3) \times {3}^{5x + 1}$

23

$(3 {(3x + 1)}^{ - 1} ) '= - 3 {(3x + 1)}^{ - 2} \times 3 = - \frac{9}{ {(3x + 1)}^{2} }$