Question

Найдите производные функций

Answer 1

а)

$y' = \frac{33 \cos(33x) \times \sin(31x) - 31\cos(31x) \times ( \sin(33x) - 32)}{ { \sin }^{2}(31x) } \\$

б)

$y' = - 31 {e}^{ - 31x} \times tg(33x) + \frac{1}{ { \cos }^{2} (33x)} \times 33 {e}^{ - 31x} = \\ = \frac{e}{ - 31x} ( - 31tg(33x) + \frac{33}{ { \cos}^{2}(33x) } )$

в)

$y '= \frac{1}{33x} \times 33 \times \cos(32x) - \sin(32x) \times 32 \times ln(33x) = \\ = \frac{ \cos(32x) }{x} - 32 \sin(32x) \times ln(33x)$