Question

95 баллов, за решение всех производных функций.

Answer 1

Ответ:

1.

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

2.

$f'(x) = \frac{1}{8} \times ( - 16) {x}^{ - 17} = - \frac{2}{ {x}^{17} }$

3.

$f'(x) = (3 {x}^{ - 1} ) '= - 3 {x}^{ - 2} = - \frac{3}{ {x}^{2} }$

4.

$f'(x) = (13 {x}^{ \frac{1}{2} } )' = 13 \times \frac{1}{2} {x}^{ - \frac{1}{2} } = \frac{13}{2 \sqrt{x} }$

5.

$f'(x) = 0$

6.

$f'(x) = 7 \times 9 {x}^{8} - 2 \times 7 {x}^{6} + 4 {x}^{3} + 2x - \frac{1}{10} + 0 = \\ = 63 {x}^{8} - 14 {x}^{6} + 4 {x}^{3} + 2x - 0.1$

7.

$f'(x) = - \frac{1}{ \sin {}^{2} (x) } - \sin(x) + 3 \cos(x)$

8.

$f'(x) = \frac{1}{ \cos {}^{2} (x) } + 10 {x}^{9}$

9.

$f'(x) = - \sin(x) - (8 {x}^{ - 1} ) '- 5 = \\ = - \sin(x) + 8 {x}^{ - 2} - 5 = - \sin(x) + \frac{8}{ {x}^{2} } - 5$

10.

$f'(x) = ( {x}^{12} (6x + 14)) '= ( 6{x}^{13} + 14 {x}^{12} ) '= \\ = 78 {x}^{12} + 168 {x}^{11}$

11.

$f'(x) = (2x - 8)'(2 - 6x) + (2 - 6x)'(2x - 8) = \\ = 2(2 - 6x) - 6(2x - 8) = \\ = 4 - 12x - 12x + 48 = - 24x + 52$

12.

$f'(x) = (x - tgx) '\times 8x + (8x)'(x - tgx) = \\ = (1 - \frac{1}{ \cos { }^{2} (x) } ) \times 8x + 8(x - tgx)$

13.

$f'(x) = \frac{(7x - 9) ' (2 + 5x) - (2 + 5x)'(7x - 9)}{ {(5x + 2)}^{2} } = \\ = \frac{7(5x + 2) - 5(7x - 9)}{ {(5x + 2)}^{2} } = \frac{35x + 14 - 35x + 45}{ {(5x + 2)}^{2} } = \\ = \frac{59}{ {(5x + 2)}^{2} }$

14.

$f'(x) = \frac{(7 {x}^{9} + {x}^{8} - x)' \times ctgx - (ctgx)'(7 {x}^{9} + {x}^{8} - x) }{ {ctg}^{2}x } = \\ = \frac{(63 {x}^{8} + 8 {x}^{7} - 1)ctgx + \frac{7 {x}^{9} + {x}^{8} - x }{ \sin {}^{2} (x) } }{ {ctg}^{2} x}$

15.

$f'(x) = \frac{(2 \sqrt{x} )'(3 {x}^{6} - 6) - (3 {x}^{6} - 6)' \times 2 \sqrt{x} }{ {(3 {x}^{6} - 6) }^{2} } = \\ = \frac{ \frac{1}{ \sqrt{x} } (3 {x}^{6} - 6) - 18 {x}^{5} \times 2 \sqrt{x} }{ {(3 {x}^{6} - 6)}^{2} } = \\ = \frac{3 {x}^{5} \sqrt{x} - \frac{6}{ \sqrt{x} } - 36 {x}^{5} \sqrt{x} }{ {(3 {x}^{6} - 6) }^{2} } = \frac{ - 33 {x}^{5} \sqrt{x} - \frac{6}{ \sqrt{x} } }{ {(3 {x}^{6} - 6) }^{2} } = \\ = \frac{1}{(3 {x}^{6} - 6) {}^{2} } \times ( \frac{ - 33 {x}^{6} - 6 }{ \sqrt{x} } ) = \\ = - \frac{33 {x}^{6} + 6 }{ \sqrt{x} {(3 {x}^{} }^{6} - 6) {}^{2} }$

16.

$f'(x) = 12 {(2x + 5)}^{11} \times (2x + 5) '= \\ = 12 {(2x + 5)}^{11} \times 2 = 24 {(2x + 5)}^{11}$

17.

$f'(x) = ({( {x}^{18} - {x}^{4} + 6)}^{ \frac{1}{2} } ) '= \\ = \frac{1}{2} {( {x}^{8} - {x}^{4} + 6) }^{ - \frac{1}{2} } \times ( {x}^{8} - {x}^{4} + 6)' = \\ = \frac{8 {x}^{7} - 4 {x}^{3} }{2 \sqrt{ {x}^{8} - {x}^{4} + 6 } } = \frac{4 {x}^{7} - 2 {x}^{3} }{ \sqrt{ {x}^{8} - {x}^{4} + 6} }$

18.

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

19.

$f'(x) = - \sin(10x) \times (10x) '= - 10 \sin(10x)$

20.

$f'(x) = \frac{1}{ \cos {}^{2} (7x - \frac{\pi}{6} ) } \times (7x - \frac{\pi}{6} )' = \frac{7}{ \cos {}^{2} (7x - \frac{\pi}{6} ) }$

21.

$f'(x) = \frac{1}{2} {(2x - 5)}^{ - \frac{1}{2} } \times 2 + ( {x}^{4} ) '= \\ = \frac{1}{ \sqrt{2x - 5} } + 4 {x}^{3}$