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.