Question

Найти производную функции

Answer 1

Ответ:

$y' = 0 + \frac{1} { 6} \times \frac{( { \sin }^{2} (6x))' \cos(12x) - ( \cos(12x))' \times { \sin }^{2} (6x)}{ { \cos }^{2} (12x)} = \\ = \frac{1}{6} \times \frac{2 \sin(6x) \cos(6x) \times 6 \times \cos(12x) + \sin(12x) \times 12 \times { \sin }^{2} (6x)}{ { \cos }^{2} (12x)} = \\ = \frac{1}{6} \times \frac{6 \times \sin(12x) \cos(12x) + 12 \sin(12x) { \sin}^{2} (6x)}{ { \cos }^{2}(12x) } = \\ = \frac{1}{6} \times (\frac{6 \sin(12x) }{ \cos(12x) } + \frac{12 \sin(12) { \sin }^{2} (6x) }{ { \cos }^{2}(12x) } ) = \\ = tg(12x) + \frac{2tg(12x) { \sin }^{2}(6x) }{ \cos(12x) }$