Question

Решить производную
(cos x*(1+sin x))`

Answer 1

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