Question

Найти производную решите​

Answer 1

Ответ:

1

$y' = 3 {( {x}^{5} + ln(x)) }^{2} \times ( {x}^{5} + ln(x))' = \\ = 3 {( {x}^{5} + ln(x)) }^{2} \times (5 {x}^{4} + \frac{1}{x} )$

2

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

3

$y '= (tgx)' \times ctgx + (ctgx) '\times tgx = \\ = \frac{1}{ \cos {}^{2} (x) } \times ctgx - \frac{1}{ \sin {}^{2} (x) } \times tgx = \\ = \frac{1}{ \cos {}^{2} (x) } \times \frac{ \cos(x) }{ \sin(x) } - \frac{1}{ \sin {}^{2} (x) } \times \frac{ \sin(x) }{ \cos(x) } = \\ = \frac{1}{ \sin(x) \cos(x) } - \frac{1}{ \sin(x) \cos(x) } = 0$