Question

Решите примеры Тема: "Производная функция" (с подробным решением

Answer 1

1.

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

2.

$f(x) = 3x - \sqrt{x} - 12 = \\ = 3x - {x}^{ \frac{1}{2} } - 12 \\ f'(x) = 3 - \frac{1}{2} {x}^{ - \frac{1}{2} } - 0 = 3 - \frac{1}{2 \sqrt{x} }$

3.

$f'(x) = 3 {x}^{2} - 2 \times 7 {x}^{6} + 2 \times ( - 1) {x}^{ - 2} - \cos(x) + 7 - 0 = \\ = 3 {x}^{2} - 14 {x}^{6} - \frac{2}{ {x}^{2} } - \cos(x) + 7$

4.

$f'(x) = (3x + 8)'(2 + 4x) + (2 + 4x)'(3x + 8) = \\ = 3(2 + 4x) + 4(3x + 8) = \\ = 6 + 12x + 12x + 24 = 24x + 30$

5.

$f'(x) = \frac{(3x + 8)'(2 + 4x) - (2 + 4x)'(3x + 8)}{ {(2 + 4x)}^{2} } = \\ = \frac{3(2 + 4x) - 4(3x + 8)}{ {(2 + 4x)}^{2} } = \frac{6 + 12x - 12x - 24}{ {(2 + 4x)}^{2} } = \\ = - \frac{18}{ {(2x + 4)}^{2} }$