Question

ПОМОГИТЕ ПОЖАЛУЙСТА, ДАЮ 100 БАЛЛОВ

Answer 1

Ответ:

1.

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

$f'(x) = 2(3x - 1) \times (3x - 1)' = \\ = 2(3x - 1) \times 3 = 6(3x - 1) = \\ = 18x - 6$

2.

$f(x) = 2 - (1 + 2x) {}^{ - 4}$

$f'(x) = 0 - ( - 4) {(1 + 2x)}^{ - 5} \times (1 + 2x) '= \\ = 4 {(1 + 2x)}^{ - 5} \times 2 = \frac{8}{ {(1 + 2x)}^{5} }$

3.

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

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

4.

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

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