Question

Вычислите производную функции

Answer 1

1.

$y' = 2x + 3$

2.

$y' = (2 \times {x}^{ - 2} )' + ( {x}^{ \frac{2}{3} } )' = \\ = - 4 {x}^{ - 3} + \frac{2}{3} {x}^{ - \frac{1}{3} } = \\ = - \frac{4}{ {x}^{3} } + \frac{2}{3 \sqrt[3]{x} }$

3.

$y' = 2cosx - \frac{1}{x ln2 }$

4.

$y' = ({x}^{2} )' \times lnx + {x}^{2} \times (lnx) ' = \\ =2xlnx + {x}^{2} \times \frac{1}{x} = \\ = 2xlnx + x$

5.

$y' = \frac{ ({x}^{2} + 4) ' \times( {x}^{2} - 1) - ({x}^{2} + 4) \times( {x}^{2} - 1) ' }{ {( {x}^{2} - 1) }^{2} } = \\ = \frac{2x( {x}^{2} - 1) - 2x( {x}^{2} + 4)}{ {( {x}^{2} - 1) }^{2} } = \\ = \frac{2 {x}^{3} - 2x - 2 {x}^{3} - 8x}{{( {x}^{2} - 1) }^{2}} = \\ = - \frac{ 10x }{{( {x}^{2} - 1) }^{2}}$