Question

Найдите производные заданной функции​

Answer 1

а

$f'(x) = \sqrt{2} \times 2x - ((3x - 2)(5x + 1)) '= \\ = 2 \sqrt{2} x - (15 {x}^{2} + 3x - 10x - 2)' = \\ = 2 \sqrt{2} x - (15 {x}^{2} - 7x - 2)' = \\ = 2 \sqrt{2} x - (30x - 7) = \\ = 2 \sqrt{2} - 30x + 7 =(2 \sqrt{2} + 30)x - 7$

б

$f'(x) = \frac{( {x}^{2})'( {x}^{4} + 1) - ( {x}^{4} + 1)' \times {x}^{2} }{ {( {x}^{4} + 1) }^{2} } = \\ = \frac{2x( {x}^{4} + 1) - 4 {x}^{3} \times {x}^{2} }{ {( {x}^{4} + 1)}^{2} } = \\ = \frac{2 {x}^{5} + 2x - 4 {x}^{5} }{ {( {x}^{4} + 1)}^{2} } = \frac{2x - 2 {x}^{4} }{ {( {x}^{4} + 1)}^{2} }$

с

$f'(x) = - 5 {x}^{ - 6} + ( {x}^{ \frac{5}{2} } )' - 0 = \\ = - \frac{5}{ {x}^{6} } + \frac{5}{2} {x}^{ \frac{3}{2} } = - \frac{5}{ {x}^{6} } + 2.5x \sqrt{x}$