Дана функция f(x)=sin3x*cos3x. Найдите f'(x).

Question

Дана функция f(x)=sin3x*cos3x. Найдите f'(x).

Answer 1

F(x) = sin3x·cos3x
f '(x) = (sin3xcos3x)' = (sin3x)'· cos3x + (cos3x)'· sin3x =
= 3cos3x·cos3x - 3sin3x·sin3x = 3cos² 3x - 3sin² 3x = 3(cos² 3x - sin² 3x) =
= 3cos6x