Question

найти производные фунций

Answer 1

Ответ:

$1)y' = 2x \sin(x) + {x}^{2} \cos(x) + 2 \cos(x) - 2x \sin(x) - 2 \cos(x) = \\ = {x}^{2} \cos(x)$

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

$3)y' = \frac{ - \sin(x) \times (2 - 3 \sin(x)) + 3 \cos(x) \times \cos(x) }{ {(2 - 3 \sin(x)) }^{2} } = \\ = \frac{ - 2 \sin((x) + 3 { \sin}^{2}x + 3 { \cos }^{2}x }{ {(2 - 3 \sin(x)) }^{2} } = \frac{3 - 2 \sin(x) }{ {(2 - 3 \sin(x)) }^{2} }$

$4)y '= \frac{1}{1 + 2 \cos(3x) } \times ( - 3 \sin(3x)) = \\ = - \frac{3 \sin(3x) }{1 + 2 \cos(3x) }$