Question

Найдите производные функции

Answer 1

Ответ:

1.

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

2.

$y' = ( {x}^{3} - 2)'( 2{x}^{3} + 1) + (2 {x}^{3} + 1)'( {x}^{3} - 2) = \\ = 3 {x}^{2} (2 {x}^{3} + 1) + 6 {x}^{2} ( {x}^{3} - 2) = \\ = 6 {x}^{5} + 3 {x}^{2} + 6 {x}^{5} - 12 {x}^{2} = \\ = 12 {x}^{5} - 9 {x}^{2}$

3.

$y '= ( {x}^{3} )'(3x + 2) + (3x + 2) '\times {x}^{3} = \\ = 3 {x}^{2} (3x + 2) + 3 {x}^{3} = \\ = 9 {x}^{3} + 3 {x}^{2} + 3 {x}^{3} = 12 {x}^{3} + 3 {x}^{2}$

4.

$y' = (3 {x}^{2} - 4)'(7 {x}^{2} + x - 1) + ( 7{x}^{2} + x - 1)'(3 {x}^{2} - 4) = \\ = 6x(7 {x}^{2} + x - 1) + (14x + 1)(3 {x}^{2} - 4) = \\ = 42 {x}^{3} + 6 {x}^{2} - 6x + 42 {x}^{3} - 56x + 3 {x}^{2} - 4 = \\ = 64 {x}^{3} + 9 {x}^{2} - 62x - 4$