Question

найдите производные
Знайдіть похідну

Answer 1

Ответ:

а

$y' = ( - 2x)' \times \sin(x) + ( \sin(x)) ' \times ( - 2x) = \\ = - 2 \sin(x) - 2x \cos(x)$

б

$y' = \frac{(2x - 3 {x}^{2} )' \times (3x - 4) - (3x - 4) '\times (2x - 3 {x}^{2}) }{{(3x - 4)}^{2} } = \\ = \frac{(2 - 6x)(3x - 4) - 3(2x - 3 {x}^{2}) }{ {(3x - 4)}^{2} } = \\ = \frac{6x - 8 - 18 {x}^{2} + 24x - 6x + 9 {x}^{2} }{ {(3x - 4)}^{2} } = \\ = \frac{ - 9 {x}^{2} + 24x - 8 }{ {(3x - 4)}^{2} }$

в

$y' = 2 \times 6{(3 {x}^{5} - x)}^{5} \times (3 {x}^{5} - x)' = \\ = 12 {(3 {x}^{5} - x) }^{5} \times (15 {x}^{4} - 1)$

г

$y' = 15 {ctg}^{14} ( \frac{4x}{15} ) \times ( - \frac{1}{ \sin {}^{2} ( \frac{4x}{15} ) } ) \times \frac{4}{15} = \\ = - 4 {ctg}^{14} ( \frac{4x}{15} ) \times \frac{1}{ \sin {}^{2} ( \frac{4x}{15} ) }$