Question

производная функция помогите пожалуйста ​

Answer 1

Ответ:

17

$f'(x )= \frac{1}{2} {(4 {x}^{16} + {x}^{3} + 7) }^{ - \frac{1}{2} } \times (64 {x}^{15} + 3 {x}^{2} + 0) = \\ = \frac{(6 4{x}^{15} + 3 {x}^{2} )}{2 \sqrt{4 {x}^{16} + {x}^{3} + 7} }$

18

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

19

$f'(x) = - 12 \sin(x)$

20

$f'(x) = \frac{1}{ { \cos}^{2} (9x - \frac{\pi}{4}) } \times 9$

21

$f'(x) = ({(5 - x - 2x)}^{ - 4} + {x}^{3} ) '= \\ = ( {(5 - 3x)}^{ - 4} + {x}^{3} )' = \\ = - 4 {(5 - 3x)}^{ - 4} \times (5 - 3x) + 3{x}^{2} = \\ = \frac{12}{ {(5 - 3x)}^{4} } + 3 {x}^{2}$

2.

$f'(x) = 16 {x}^{3} - 12x \\ f'( - 2) = 16 \times ( - 8) + 24 = - 128 + 24 = - 104 \\ f'( \frac{1}{5} ) = 16 \times \frac{1}{125} - \frac{12}{5} = \frac{16 - 300}{125} = - \frac{284}{125}$