Question

Дана функция y=lntgx. Найдите её производную при x=п/12

Answer 1

$(lntan x)'=frac{1}{tan x}*frac{1}{cos^2 x}=frac{cos x}{sin x}*frac{1}{cos^2 x}=frac{1}{cos xsin x}=$

$=frac{2}{2cos xsin x}=frac{2}{sin 2x}$

$y'(frac{pi}{12})=frac{2}{sin 2x}=frac{2}{sin (2*frac{pi}{12})}=frac{2}{sin (frac{pi}{6})}=$

$=frac{2}{frac{1}{2}}=2*2=4$

Ответ: 4.