Question

Даю 35 баллов номер 2 а и б

Answer 1

Ответ:

2.

а)

$y '= - \sin( \frac{x}{3} + \frac{\pi}{4} ) \times ( \frac{x}{3} + \frac{\pi}{4} ) '= \\ = - \sin( \frac{x}{3} + \frac{\pi}{4} ) \times \frac{1}{3} \\ \\ y'( \frac{\pi}{4} ) = - \frac{1}{3} \sin( \frac{\pi}{12} + \frac{\pi}{4} ) = - \frac{1}{3} \sin( \frac{\pi}{3} ) = \\ = - \frac{1}{3} \times \frac{ \sqrt{3} }{2} = - \frac{ \sqrt{3} }{6}$

б)

$y' = \frac{1}{4} \times 4 {x}^{3} - \frac{1}{3} \times 3 {x}^{2} + 4x - 1 + 0 = \\ = {x}^{3} - {x}^{2} + 4x - 1 \\ \\ y'(1) = 1 - 1 + 4 - 1 = 3$