Question

Найдите производную.

Answer 1

Ответ:

1.

$y' = 0$

2.

$y' = 6 \times 9 {x}^{8} - 7 - 0 = 54 {x}^{8} - 7$

3.

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

4.

$y' = {e}^{4x + 1} \times (4x + 1)' + 4 \times 3 {x}^{2} = \\ = 4 {e}^{4x + 1} + 12 {x}^{2}$

5.

$y' = ln(3) \times {3}^{x} - ( - 3) {x}^{ - 4} = \\ = ln(3) \times {3}^{x} + \frac{3}{ {x}^{4} }$

6.

$y' = \frac{4}{x} + ln(3) \times {3}^{x}$

7.

$y' = \cos(x) - 0 = \cos(x)$

8.

$y' = ( {x}^{2} + 2)'( {x}^{3} - x) + ( {x}^{3} - x)'( {x}^{2} + 2) = \\ = 2x( {x}^{3} - x) + (3 {x}^{2} - 1)( {x}^{2} + 2) = \\ = 2 {x}^{4} - 2 {x}^{2} + 3 {x}^{4} + 6 {x}^{2} - {x}^{2} - 2 = \\ = 5 {x}^{4} + 3 {x}^{2} - 2$

9.

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