Question

Производная функции!!

Answer 1

Ответ:

$y = { \cos}^{2} ( \frac{x}{4} )$

$y' = 2 \cos( \frac{x}{4} ) \times ( - \sin( \frac{x}{4} ) ) \times \frac{1}{4} = \\ = - \frac{1}{4} \sin( \frac{x}{4} \times 2 ) = \\ = - \frac{1}{4} \sin( \frac{x}{2} )$

$y'' = - \frac{1}{4} \cos( \frac{x}{2} ) \times \frac{1}{2} = \\ = - \frac{1}{8} \cos( \frac{x}{2} )$

$y''' = - \frac{1}{8} \times ( - \sin( \frac{x}{2} ) ) \times \frac{1}{2} = \\ = \frac{1}{16} \sin( \frac{x}{2} )$