Question

РЕШИТЕ МАТЕШУ ДАЮ 50 БАЛЛОВ​

Answer 1

1.

$y '= 24 {x}^{3} - 15 {x}^{2} + 8x + 3 \\ y'' = 72 {x}^{2} - 30x + 8 \\ y''(1) = 72 - 30 + 8 = 50$

2.

$y' = 7 {(4x - 1)}^{6} \times (4x - 1) '= \\ = 7 {(4x - 1)}^{6} \times 4 = 28 {(4 - 1)}^{6}$

3.

$y '= \frac{1}{5x + 3} \times (5x + 3) '= \frac{5}{5x + 3}$

4.

$y' = \cos(13x) \times (13x)' = 13 \cos(13x)$

5.

$y' = 2 {e}^{5x} \times 5 - \frac{4}{x} + \frac{1}{7} {x}^{ - \frac{6}{7} } = \\ = 10 {e}^{5x} - \frac{4}{x} + \frac{1}{7 \sqrt[7]{ {x}^{6} } }$

6.

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

7.

$y' = ( {x}^{3} ) '\sin(5x) + ( \sin(5x))' \times {x}^{3} = \\ = 3 {x}^{2} \sin(5x) + 5 \cos(5x) \times {x}^{3} = \\ = 3 {x}^{2} \sin(5x) + 5 {x}^{3} \cos(5x)$

8.

$y' = \frac{(5x + 7)'(x - 3) - (x - 3)'(5x + 7)}{ {(x - 3)}^{2} } = \\ = \frac{5(x - 3) - (5x + 7)}{ {(x - 3)}^{2} } = \frac{5x - 15 - 5x - 7}{ {(x - 3)}^{2} } = \\ = - \frac{22}{ {(x - 3)}^{2} }$

9.

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