Question

Вычислите производную функции:
А) y=(6x^3-2x^2+7x-4)^6
Б) y=ctg^2(5x-Пи/6)

Answer 1

Ответ:

a

$y '= 6 {(6 {x}^{3} - 2 {x}^{2} + 7x - 4) }^{5} \times (6 {x}^{3} - 2 {x}^{2} + 7x - 4) '= \\ = 6 {(6 {x}^{3} - 2 {x}^{2} + 7x - 4) }^{5} (18 {x}^{2} - 4x + 7)$

b

$y' = 2ctg(5x - \frac{\pi}{6} ) \times (ctg(5x - \frac{\pi}{6}) '\times (4x - \frac{\pi}{6} ) '= \\ = 2ctg(5x - \frac{\pi}{6}) \times ( - \frac{1}{ \sin {}^{2} (5x - \frac{\pi}{6} ) } \times 5 = \\ = - \frac{10ctg(5x - \frac{\pi}{6} )}{ \sin {}^{2} (5x - \frac{\pi}{6} ) }$