Question

Найдите производную в данных произведениях

Answer 1

Ответ:

$(3 {tg}^{4} (2x)) '= 3 \times 4 {tg}^{3} (2x) \times (tg(2x))' \times (2x) '= \\ = 12 {tg}^{3} (2x) \times \frac{1}{ \cos {}^{2} (2x) } \times 2 = \frac{24 {tg}^{3} (2x)}{ \cos {}^{2} (2x) }$

$\\ ( \cos {}^{2} ( \frac{x}{2} + \frac{\pi}{4} ) )' = 2 \cos( \frac{x}{2} + \frac{\pi}{4} ) \times (\cos( \frac{x}{2} + \frac{\pi}{4} ) )' \times ( \frac{x}{2} + \frac{\pi}{4} )' = \\ = 2 \cos( \frac{x}{2} + \frac{\pi}{4} ) \sin( \frac{x}{2} + \frac{\pi}{4} ) \times \frac{1}{2} = \\ = \frac{1}{2} \sin(2( \frac{x}{2} + \frac{\pi}{4} ) ) = \frac{1}{2} \sin(x + \frac{\pi}{2} ) = \frac{1}{2} \cos( x )$