Question

Нужна помощь с решением производных ​

Answer 1

Ответ:

$1)y' = (24 {x}^{3} )' \times \sin(x) + ( \sin(x) )' \times 24 {x}^{3} = 102 {x}^{2} \sin(x) + 24 {x}^{3} \cos(x)$

$2)y' = 72 {x}^{3} \cos(x) - \sin(x) \times 18 {x}^{4}$

$3)y' = \frac{(5 {x}^{3} + 8x)' \times (7 {x}^{4} - 4 {x}^{2} ) - (7 {x}^{4} - 4 {x}^{2} )' \times (5 {x}^{3} + 8x)}{ {(7 {x}^{4} - 4 {x}^{2}) }^{2} } = \frac{(15 {x}^{2} + 8) \times (7 {x}^{4} - 4 {x}^{2} ) - (28 {x}^{3} - 8x ) \times (5 {x}^{3} + 8x) }{ {(7 {x}^{4} - 4 {x}^{2}) }^{2} } = \frac{ - 35 {x}^{6} - 188 {x}^{4} + 32 {x}^{2} }{ {(7 {x}^{4} - 4 {x}^{2}) }^{2} }$

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