Найдите производную функции y=sin3x-cos3x и вычислите ее значение при x=3 п/4

Дана функция f (x) = sin (3⋅x) - cos (3⋅x) Производная её равна: f′ (x) = (sin (3⋅x) - cos (3⋅x)) ′ = = (sin (3⋅x)) ′ - (cos (3⋅x)) ′ = = cos (3⋅x) ⋅ (3⋅x) ′ - (-sin (3⋅x)) ⋅ (3⋅x) ′ = = cos (3⋅x) ⋅3 - (-sin (3⋅x)) ⋅3 Ответ: f′ (x) = cos (3⋅x) ⋅3 - (-sin (3⋅x)) ⋅3 = 3 (sin (3x) + cos (3x)).

Значение производной при х = (3 π/4) :

f′ (3π/4) = 3 (sin (9π/4) + cos (9π/4)) = 3 (sin (π/4) + cos (π/4)) =

= 3 ((√2/2) + (√2/2)) = 3√2.