Question

1-2 примеры.
отдаю все балы.
помогите, пожалуйста, очень очень очень срочно!)​

Answer 1

Ответ:

1

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

$f'(2) = 5(4 - 4 - 2) {}^{4} \times 2 = 10 \times 16 = 160$

2

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

$f'(1) = \frac{2 \times {3}^{3} }{1} = 2 \times 27 = 54$

3

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

$f'( - 1) = \frac{ - 8 - 5}{2 \times 3} = - \frac{13}{6}$

4

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

$f'(3) = \frac{1}{1} - \frac{3 \times ( - 1)}{1} = 1 + 3 = 4$