Question

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Answer 1

Ответ:

1 .

$y' = - 18 {x}^{5} + 7 \\ dy = ( - 18 {x}^{5} + 7) dx$

2.

$y' = - \sin( {x}^{2} + 2 ) \times 2x = \\ = - 2x \sin( {x}^{2} + 2) \\ dy = - 2x \sin( {x}^{2} + 2 ) dx$

3.

$y' = - \frac{1}{ { \sin}^{2}(5x) } \times 5 \\ dy = - \frac{5}{ { \sin}^{2}(5x) } dx$

4.

$y' = {e}^{3 {x}^{2} - 4 } \times 6x \\ dy = 6x {e}^{3 {x}^{2} - 4 } dx$

5.

$y' = ln(8) \times {8}^{3x + 2} \times 3 \\ dy = 3 ln(8) \times {8}^{3x + 2} dx$

6.

$y' = \frac{1}{3x + 2} \times 3 \\ dy = \frac{3}{3x + 2} dx$

7.

$y' = \frac{1}{1 + 16 {x}^{2} } \times 4 \\ dy = \frac{4}{1 + 16 {x}^{2} } dx$

8.

$y '= \frac{1 \times (3 {x}^{2} - 1) - 6x(2 + x) }{ ({3 {x}^{2} - 1) } ^{2} } = \\ = \frac{3 {x}^{2} - 1 - 12x - 6 {x}^{2} }{ {(3 {x}^{2} - 1)}^{2} } = \\ = \frac{ - 3 {x}^{2} - 12x - 1}{ {(3 {x}^{2} - 1) }^{2} } = \\ = - \frac{3 {x}^{2} + 12x + 1}{ {(3 {x}^{2} - 1) }^{2} } \\ \\ dy = - \frac{3 {x}^{2} + 12x + 1 }{ {(3 {x}^{2} }^{2} - 1) } dx$

9.

$y' = 2 \cos(2x) \times {e}^{ {x}^{2} } + {e}^{ {x}^{2} } \times 2x \times \sin(2x) = \\ = {e}^{ {x}^{2} } (2 \cos(2x) + 2x \sin(2x)) \\ \\ dy = 2 {e}^{ {x}^{2} }( \cos(2x) + x \sin(2x)) dx$