Question

Найти производную функцию

Answer 1

Ответ:

а

$y' = 6 {( {x}^{2} - 3x) }^{5} \times ( {x}^{2} - 3x)' = \\ = 6(2x - 3) {( {x}^{2} - 3x) }^{5} = \\ = (12x - 18) {( {x}^{2} - 3x) }^{5}$

б

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

$y' = - 2 {( {x}^{2} - 3x) }^{ - 2} \times ( {x}^{2} - 3x) '= \\ = - \frac{2(2x - 3)}{ {( {x}^{2} - 3x)}^{2} } = - \frac{4x - 6}{ {( {x}^{2} - 3x)}^{2} }$

в

$y = \sqrt{ \sin(7x) - 5x} = {( \sin(7x) - 5x) }^{ \frac{1}{2} }$

$y '= \frac{1}{2} {( \sin(7x) - 5x) }^{- \frac{1}{2} } \times (\sin(7x) - 5x) '= \\ = \frac{7 \cos(7x) - 5 }{2 \sqrt{ \sin(7x) - 5x) } }$