Question

Найти производную функцию СРОЧНО даю 100 балов

Answer 1

1)

$y = {x}^{18} \\ y' = ( {x}^{18} )' = 18 {x}^{17}$

2)

$y = {x}^{ - 9} \\ y' = ( {x}^{ - 9} )' = - 9 {x}^{ - 10} = - \frac{9}{ {x}^{10} }$

3)

$y = {x}^{0.52} \\ y' = ( {x}^{0.52} )' = 0.52 {x}^{ - 0.48}$

4)

$y = {x}^{ \frac{2}{9} } \\ y' = ( {x}^{ \frac{2}{9} } )' = \frac{2}{9} {x}^{ - \frac{7}{9} }$

5)

$y = {x}^{ - \frac{3}{5} } \\ y' = - \frac{3}{5} {x}^{ - \frac{8}{5} }$

6)

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

7)

$y = \frac{1}{ \sqrt[10]{x} } \\ y' = ( {x}^{ - \frac{1}{10} } )' = - \frac{1}{10} {x}^{ - \frac{11}{10} } = - \frac{1}{10 \sqrt[10]{ {x}^{11} } }$

8)

$y = (9 - 4x) {}^{7} \\ y' = ((9 - 4x) {}^{7} )' = (9 - 4x)'( {g}^{7} )' = - 4 \times 7 {g}^{6} = \\ = - 28 {(9 - 4x)}^{6}$

9)

$y = (5x + 8) {}^{ - 4} \\ y' = (5x + 8)' ({g}^{ - 4} )' = 5 \times ( - 4) {g}^{ - 5} = \\ = - 20(5x + 8) {}^{ - 5}$

10)

$y = \sqrt[6]{(5 - 3x) {}^{5} } \\ y' = ((5 - 3x) {}^{ \frac{5}{6} } )' = (5 - 3x)'( {g}^{ \frac{5}{6} } )' = \\ = - 3 \times \frac{5}{6} {g}^{ - \frac{1}{6} } = - \frac{5}{2} (5 - 3x) {}^{ - \frac{1}{6} } = - \frac{5}{2 \sqrt[6]{5 - 3x} }$