Question

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

Answer 1

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