Найти производную функций:

1: (x+3) * x^3

2: (x-4) * 3x^2

1. f′ (x) = ((x+3) ⋅x3) ′ = (x+3) ′⋅x3 + (x+3) ⋅ (x3) ′=

=1⋅x3 + (x+3) ⋅3⋅x2=x3 + (x+3) ⋅3⋅x2

Ответ:

f′ (x) = x3 + (x+3) ⋅3⋅x2

2. f′ (x) = ((x-4) ⋅3⋅x2) ′ = ((x-4) ⋅3) ′⋅x2 + (x-4) ⋅3⋅ (x2) ′ = = 3⋅ (x-4) ′⋅x2 + (x-4) ⋅6⋅x=

=3⋅1⋅x2 + (x-4) ⋅6⋅x = 3⋅x2 + (x-4) ⋅6⋅x

Ответ:

f′ (x) = 3⋅x2 + (x-4) ⋅6⋅x