Question

Найдите производную пожалуйста

Answer 1

Ответ:

$y' = \frac{2 \sin(x) \times \cos(x) (2 + 3 { \cos(x) }^{2}) - 6 \cos(x) \times ( - \sin(x)) \times { \sin(x) }^{2} }{ {(2 + 3 { \cos(x) }^{2}) }^{2} } =\\ \frac{2 \sin(x) \cos(x) (2 + 3 { \cos(x) }^{2} + 3 { \sin(x) }^{2} ) }{ {(2 + 3 { \cos(x) }^{2}) }^{2} } = \\ \frac{ \sin(2x) \times (2 + 3)}{ {(2 + 3 { \cos(x) }^{2}) }^{2} } = \frac{5 \sin(2x) }{ {(2 + 3 { \cos(x) }^{2} )}^{2} }$