Question

С производной Вычисли f'(2П) f(x) = 4 tg 0,5 x срочно-срочно

Answer 1

$f'(x)=(4tg(0.5x))'=4(tg(0.5x))'=4 *\frac{1}{cos^2(0.5x)}*(0.5x)'=$
$=4 *\frac{1}{cos^2(0.5x)}*0.5= \frac{2}{cos^2(0.5x)}$

$f'(2\pi)=\frac{2}{cos^2(0.5*2\pi)} =\frac{2}{cos^2(\pi)}= \frac{2}{(-1)^2}=2$