Question

1)Найдите производную функции:f(x)=(5+3x)^3
2)Укажите первообразную функции:f(x)=3x^2+2x-4

Answer 1

1)
f ' (x) = ((3x + 5)^3)' = 3(3x + 5)^2 (3x + 5)' = 9(3x + 5)^2

2)
F(x) = ∫ (3x^2 + 2x - 4) dx = 3∫x^2 dx + 2∫x dx - 4∫ 1 dx = 
= 3x^3/3 + 2x^2/2 - 4x + C =
= x^3 + x^2 - 4x + C