Question

Решите пожалуйста примеры.Найти производную функции.

Answer 1

Ответ:

1

$y = \frac{4}{3} {x}^{ - \frac{3}{5} }$

$y '= \frac{4}{5} \times ( - \frac{3}{5} ) {x}^{ - \frac{8}{5} } = - \frac{12}{25x \sqrt[5]{ {x}^{3} } }$

2

$y = 2 \sqrt[5]{ {x}^{3} } = 2 {x}^{ \frac{3}{5} }$

$y' = 2 \times \frac{3}{5} {x}^{ - \frac{2}{5} } = \frac{6}{5 \sqrt[5]{ {x}^{2} } }$

3

$y = \frac{ 3\sqrt{x} }{ {x}^{2} } = \frac{3 {x}^{ \frac{1}{2} } }{ {x}^{2} } = 3 {x}^{ \frac{1}{2} - 2} = 3 {x}^{ - \frac{3}{2} }$

$y' = 3 \times ( - \frac{3}{2} ) {x}^{ - \frac{5}{2} } = - \frac{9}{2 {x}^{2} \sqrt{x} }$

4

$y = \frac{7 \sqrt[3]{x} }{ \sqrt{x} } = \frac{7 {x}^{ \frac{1}{3} } }{ {x}^{ \frac{1}{2} } } = 7 {x}^{ \frac{1}{3} - \frac{1}{2} } = 7 {x}^{ - \frac{1}{6} }$

$y' = 7 \times ( - \frac{1}{6} ) {x}^{ - \frac{7}{6} } = - \frac{7}{6x \sqrt[6]{x} }$

5

$f(x)= \frac{1}{ {x}^{4} } = {x}^{ - 4} \\ f'(x) = - 4 {x}^{ - 5} = - \frac{4}{ {x}^{5} } \\ f'( \frac{1}{2} ) = - 4 \times \frac{1}{ {( \frac{1}{2}) }^{5} } = - 4 \times {2}^{5} = \\ = - 4 \times 32 = - 128$