Question

Найдите производную функцию

Answer 1

1)

$y = {x}^{24} \\ y' = ( {x}^{24} )' = 24 {x}^{23}$

2)

$y = {x}^{ - 25} \\ y' = ( {x}^{ - 25} )' = -25{x}^{ - 26} = - \frac{25}{ {x}^{26} }$

3)

$y = {x}^{0.75} \\ y' = ( {x}^{0.75} )' = 0.75 {x}^{ - 0.25}$

4)

$y = {x}^{ \frac{6}{11} } \\ y' = ( {x}^{ \frac{6}{11} } )' = \frac{6}{11} {x}^{ - \frac{5}{11} }$

5)

$y = {x}^{ - \frac{3}{8} } \\ y' = - \frac{3}{8} {x}^{ - \frac{11}{8} }$

6)

$y = \sqrt[5]{ {x}^{11} } \\ y' = ({x}^{ \frac{11}{5} } )' = \frac{11}{5} {x}^{ \frac{6}{5} }$

7)

$y = \frac{1}{ \sqrt[9]{x} } \\ y' = ( {x}^{ - \frac{1}{9} } )' = - \frac{1}{9} {x}^{ - \frac{10}{9} } = - \frac{1}{9 \sqrt[9]{ {x}^{10} } }$

8)

$y = (9 - 3x) {}^{4} \\ y' = ((9 - 3x) {}^{4} )' = (9 - 3x)'( {g}^{4} )' = - 3 \times 4 {g}^{3} = \\ = - 12 {(9 - 3x)}^{3}$

9)

$y = (6x - 1) {}^{ - 3} \\ y' = ((6x - 1) {}^{ - 3} )' = (6x - 1)'( {g}^{ - 3} )' = \\ = 6 \times ( - 3) {g}^{ - 4} = - 18(6x - 3) {}^{ - 4}$

10)

$y = \sqrt[5]{(5 + 3x) {}^{4} } \\ y' = ((5 + 3x) {}^{ \frac{4}{5} } )' = (5 + 3x)' ({g}^{ \frac{4}{5} } )' = \\ = 3 \times \frac{4}{5} {g}^{ - \frac{1}{5} } = \frac{12}{5} (5 + 3x) {}^{ - \frac{1}{5} }$