Вычислите y" (0) функции y=sin² 3x

y' = (sin^2 (3x)) ′ = 2 (sin (3x)) ′sin (3x) = 2 (3x) ′cos (3x) sin (3x) = 6 (x) ′cos (3x) sin (3x) = 6cos (3x) sin (3x);

y'' = (6cos (3x) sin (3x)) ' = (6cos (3x) sin (3x)) ′ = 6 (cos (3x) sin (3x)) ′ = 6cos (3x) (sin (3x)) ′+6sin (3x) (cos (3x)) ′ = - 6 (3x) ′sin^2 (3x) + 6 (3x) ′cos^2 (3x) = 18 (x) ′cos^2 (3x) - 18 (x) ′sin^2 (3x) = 18cos^2 (3x) - 18sin^2 (3x);

y'' (0) = 18cos^2 (3*0) - 18sin^2 (3*0) = 18cos^2 (0) - 18sin^2 (0) = 18*1-18*0=18.