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

[latex](\ln\tan x)'=\frac{1}{\tan x}*\frac{1}{\cos^2 x}=\frac{\cos x}{\sin x}*\frac{1}{\cos^2 x}=\frac{1}{\cos x\sin x}=[/latex] [latex]=\frac{2}{2\cos x\sin x}=\frac{2}{\sin 2x}[/latex] [latex]y'(\frac{\pi}{12})=\frac{2}{\sin 2x}=\frac{2}{\sin (2*\frac{\pi}{12})}=\frac{2}{\sin (\frac{\pi}{6})}=[/latex] [latex]=\frac{2}{\frac{1}{2}}=2*2=4[/latex] Ответ: 4.