Question

Найти производные элементарных функций, памагите ​

Answer 1

1

$(5 {x}^{4} - 3.5 {x}^{2} + x + 6) '= \\ = 5 \times 4 {x}^{3} - 3.5 \times 2x + 1 + 0 = \\ = 20 {x}^{3} - 7x + 1$

2

$(( \frac{8}{x} + {x}^{2} ) \sqrt{x})' = ( \frac{8}{x} \times \sqrt{x} + {x}^{2} \sqrt{x} ) '= \\ = (8 {x}^{ - \frac{1}{2} } + {x}^{ \frac{5}{2} } )' = 8 \times ( - \frac{1}{2} ) {x}^{ - \frac{3}{2} } + \frac{5}{2} {x}^{ \frac{3}{2} } = \\ = - \frac{4}{x \sqrt{x} } + 2.5x \sqrt{x}$

3

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