Question

только 16 числа больше не надо

Answer 1

Ответ:

1.

$y' = 3 \times 4 {x}^{3} = 12 {x}^{3}$

2.

$y' = \frac{1}{2} \times 6 {x}^{5} = 3 {x}^{5}$

3.

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

4.

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

5.

$y' = ( {x}^{ - \frac{3}{2} } )' = - \frac{3}{2} {x}^{ - \frac{5}{2} } = - \frac{3}{2 {x}^{2} \sqrt{x} }$

6.

$y' = 20 {x}^{3} - 14x - 1$

7.

$y' = 5 {x}^{4} + 6 {x}^{2} + \frac{ {x}^{ - 2} }{2} = 5 {x}^{4} + 6 {x}^{2} + \frac{1}{2 {x}^{2} }$

8.

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

9.

$y = ((x + \frac{1}{ \sqrt{x} } - \frac{1}{ {x}^{2} } )(3 {x}^{2} + x - 8) )'= \\ = (3x {}^{3} + {x}^{2} - 8x + 3x \sqrt{x} + \sqrt{x} - \frac{8}{ \sqrt{x} } - 3 - \frac{1}{x} + \frac{8}{ {x}^{2} } ) '= \\ = (3 {x}^{3} + {x}^{2} - 8x + 3 {x}^{ \frac{3}{2} } + {x}^{ \frac{1}{2} } - 8 {x}^{ - \frac{1}{2} } - 3 - {x}^{ - 1} + 8 {x}^{ - 2} ) '= \\ = 9 {x}^{2} + 2x - 8 + \frac{9}{2} {x}^{ \frac{1}{2} } + \frac{1}{2} {x}^{ - \frac{1}{2} } + 4 {x}^{ - \frac{3}{2} } - 0 + {x}^{ - 2} - 16 {x}^{ - 3} = \\ = 9 {x}^{2} + 2x - 8 + \frac{9}{2} \sqrt{x} + \frac{1}{2 \sqrt{x} } + \frac{4}{x \sqrt{x} } + \frac{1}{ {x}^{2} } - \frac{16}{ {x}^{3} }$

10.

$y' = ((x + \frac{1}{x} + \frac{1}{ {x}^{2} } )( {x}^{2} + x + 1) )'= \\ = ( {x}^{3} + {x}^{2} + x + x + 1 + \frac{1}{x} + 1 + \frac{1}{x} + \frac{1}{ {x}^{2} } )' = \\ = ( {x}^{3} + {x}^{2} + 2x + 2 + \frac{2}{x} + \frac{1}{ {x}^{2} } )' = \\ = 3 {x}^{2} + 2x + 2 + 0 - 2 {x}^{ - 2} - 2 {x}^{ - 3} = \\ = 3 {x}^{2} + 2x + 2 - \frac{2}{ {x}^{2} } - \frac{2}{ {x}^{3} }$

11.

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

12.

$y' = \frac{(x - 2)'(2 {x}^{2} - 1) - (2 {x}^{2} - 1)'(x - 2)}{ {(2 {x}^{2} - 1)}^{2} } = \\ = \frac{1 \times (2 {x}^{2} - 1) - 4x(x - 2)}{ {(x - 2)}^{2} } = \frac{2 {x}^{2} - 1 - 4 {x}^{2} + 8x}{ {(x - 2)}^{2} } = \\ = \frac{ - 2x {}^{2} + 8x - 1 }{ {(x - 2)}^{2} } = - \frac{2 {x}^{2} - 8x + 1}{ {(x - 2)}^{2} }$

13.

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

14.

$y' = 3 {(2x + 1)}^{2} \times (2x + 1)' + 10(3x - 2) \times (3x - 2)' = \\ = 3 {(2x + 1)}^{2} \times 2 + 10(3x - 2) \times 3 = \\ = 6 {(2x + 1)}^{2} + 90x - 60$

15.

$y '= ((3x + 1) {}^{ - 3} ) '= - 3 {(3x + 1)}^{ - 4} \times (3x + 1) '= \\ = - \frac{9}{ {(3x + 1)}^{4} }$

16.

$y' = ( {(5x - 1)}^{ \frac{1}{2} } ) '= \frac{1}{2} {(5x - 1)}^{ - \frac{1}{2} } \times (5x - 1) '= \frac{5}{2 \sqrt{5x - 1} }$