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.

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