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)

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