Найти производную y=5x^3 - cos^2 5x

Question

Найти производную y=5x^3 - cos^2 5x

Answer 1

Y ' = 5*3x^2 - (cos 5x * cos 5x)' = 
= 15x^2 - ( (cos5x)'cos5x + cos5x (cos5x)') = 
= 15x^2 - ( - 5sin5xcos5x - 5sin5x cos5x) =
= 15x^2  + 5sin5xcos5x + 5sin5x cos5x =
= 15x^2  + 10sin5xcos5x = 
= 15x^2 + 5 sin(10x)