Question

Найдите f'(π/2) если f(x)=-1/3 * sin(2x+π/2)

Answer 1

$f(x)= -\frac{1}{3} sin(2x+ \frac{ \pi }{2} )= \frac{1}{3} cos2x \\ \\ f'(x)= \frac{1}{3} (-sin2x)2=- \frac{2}{3}sin2x \\ \\ \\ f'( \frac{ \pi }{2} )=- \frac{2}{3} sin(2* \frac{ \pi }{2} )=- \frac{2}{3} sin \pi =0$