Question

как можно скорее ! Найдите производную сложной функции а) (4х^3+6х-3)^6
б) y=-4√2x-3x
в)y= cos^5 6x

Answer 1

а

$y = {(4 {x}^{3} + 6x - 3) }^{6}$

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

б

$y = - 4 \sqrt{2x {}^{2} - 3x} = - 4 {(2 {x}^{2} - 3x) }^{ \frac{1}{2} } \\$

$y'= - 4 \times \frac{1}{2} {(2 {x}^{2} - 3x)}^{ - \frac{1}{2} } \times (2x {}^{2} - 3x) '= \\ = - \frac{2(4x - 3)}{ \sqrt{2 {x}^{2} - 3x} }$

в

$y = \cos {}^{5} (6x)$

$y '= 5 \cos {}^{4} (6x) \times (\cos(6x) )'\times (6 x) '= \\ = 5 \cos {}^{4} (6x) \times ( - \sin(6x)) \times 6 = \\ = - 30 \sin(6x) \cos {}^{4} (6x)$