Question

решить производные функции

Answer 1

1.

$y '= \frac{ - 3(4 + {x}^{2}) - 2x \times ( - 3x) }{ {(4 + {x}^{2}) }^{2} } = \\ = \frac{ - 12 - 3 {x}^{2} + 6 {x}^{2} }{ {(4 + {x}^{2}) }^{2} } = \frac{3 {x}^{2} - 12 }{ {(4 + {x}^{2} )}^{2} }$

2.

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

3.

$y '= \frac{1}{2 \sqrt{x} } ln(x) + \frac{1}{x} \times \sqrt{x} = \\ = \frac{ ln(x) }{2 \sqrt{x} } + \frac{1}{ \sqrt{x} } = \frac{ ln(x) + 2}{2 \sqrt{x} }$

4.

$y' = - 27 {x}^{ - 4} + 5 {x}^{ - 2} = \\ = - \frac{27}{ {x}^{4} } + \frac{5}{ {x}^{2} }$

5.

$y' = 2 {x}^{ - \frac{4}{3} } + 3 = \frac{2}{x \sqrt[3]{x} } + 3 \\$

6.

$y' = 8xctgx - \frac{4 {x}^{2} }{ { \sin }^{2}(x) } \\$

7.

$y'= \frac{ - 2x(2x + 8) - 2(6 - {x}^{2} )}{ {(2x + 8)}^{2} } = \\ = \frac{ - 4 {x}^{2} - 16x - 12 + 2 {x}^{2} }{ {(2x + 8)}^{2} } = \\ = \frac{ - 2 {x}^{2} - 16x - 12}{ {(2x + 8)}^{2} }$