Question

Производная частного

Answer 1

Ответ:

$y = \frac{ {x}^{6} + \sin(x) }{ \cos(x) }$

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

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