Question

Найдите значение производной функции f(x)=4cos(2x+п/3) при х=п/3

Answer 1

$f(x)=4cos(2x+\frac{\pi }{3}\\\\f'(x)=4\cdot \Big (-sin(2x+\frac{\pi }{3})\Big )\cdot (2x+ \frac{\pi}{3})'=-4sin(2x+\frac{\pi}{3})\cdot 2\\\\f'(\frac{\pi}{3})=-8\cdot sin(2\cdot \frac{\pi}{3}+\frac{\pi}{3})=-8\cdot sin\pi =0$