Question

Найти производную функции y=(x+3)^3(x+1)

Answer 1

$y = {(x + 3)}^{3} (x + 1)$

$y' = {((x + 3)}^{2} ) '\times (x + 3)' \times (x + 1) + (x + 1)' \times {(x + 3)}^{3} = \\ = 3 {(x + 3)}^{2} \times 1 \times (x + 1) + 1 \times {(x + 3)}^{3} = \\ = {(x + 3)}^{2} (3(x + 1) + (x + 3)) = \\ = {(x + 3)}^{2} (3x + 3 + x + 3) = \\ = {(x + 3)}^{2} (4x + 6)$