Question

у=ln(tg (5x)) найти производную

Answer 1

$y = {( \tan(5x) }) \times \frac{1}{ \tan(5x) } = \frac{5}{ { \cos(5x) }^{2} } \times \frac{ \cos(5x) }{ \sin(5x) } = \frac{5}{ \sin(5x) \cos(5x) } = \frac{5}{ \frac{1}{2} \sin(10x) } = \frac{10}{ \sin(10x) }$