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))⋅3Ответ:f′(x)=cos(3⋅x)⋅3−(−sin(3⋅x))⋅3 = 3(sin(3x)+cos(3x)).
Значение производной при х = (3π/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.