Question

Найдите производную функции f(x)=tg(пи/4-x) и ее значение при x=-3/4пи

Answer 1

$f(x)=tg(\frac{\pi}{4}-x)\\\\f'(x)=\frac{1}{cos^2(\frac{\pi}{4}-x)}\cdot (-1)\\\\x=-\frac{3\pi}{4}\; ,\; f'(-\frac{3\pi}{4})=\frac{-1}{c os^2(\frac{\pi}{4}+\frac{3\pi}{4})}=\frac{-1}{cos^2\pi }=-\frac{1}{(-1)^2}=-1$

Answer 2

$f(x)=tg( \frac{\pi}{4}-x) \\ x=- \frac{3}{4}\pi \\ f'(x)= \frac{1}{cos^2( \frac{\pi}{4}-x) }(-1)= - \frac{1}{cos^2( \frac{\pi}{4}-x) } \\ f'(- \frac{3}{4}\pi)=- \frac{1}{cos^2( \frac{\pi}{4}+ \frac{3}{4}\pi ) } =- \frac{1}{(-1)^2}=-1$