Question

производные!!!
полное решение!!! решите, пожалуйста, очень нужно!!!

Answer 1

Ответ:

1.

$4 {x}^{3}$

2

$(7x - {x}^{ - 1} )' = 7 - ( - 1) {x}^{ - 2} = 7 + \frac{1}{ {x}^{2} }$

3

$( {x}^{ \frac{1}{2} } + 3x {}^{3} )' = \frac{1}{2} {x}^{ - \frac{1}{2} } + 9 {x}^{2} = \\ = \frac{1}{2 \sqrt{x} } + 9 {x}^{2}$

4

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

5

$(4x - 6)'(3 {x}^{5} + 2x - \sqrt{5}) + (3 {x}^{5} + 2x - \sqrt{5} )'(4x - 6) = \\ = 4(3 {x}^{5} + 2x - \sqrt{5} ) + (15 {x}^{4} + 2)(4x - 6) = \\ = 12 {x}^{5} + 8x - 4 \sqrt{5} + 30 {x}^{5} - 90 {x}^{4} + 8x - 12 = \\ = 42 {x}^{5} -9 0 {x}^{4} + 16x - 1 2- 4\sqrt{5}$

6

$\frac{( {x}^{3} + 5x)'( - 4x + {x}^{2}) - ( - 4x + {x}^{2})'( {x}^{3} + 5x)}{ {( {x}^{2} - 4x) }^{2} } = \\ = \frac{(3 {x}^{2} + 5)( - 4x + {x}^{2} ) - ( - 4 + 2x)( {x}^{3} + 5x)}{ {( {x}^{2} - 4x)}^{2} } = \\ = \frac{ - 12 {x}^{3} + 3 {x}^{4} - 20x + 5 {x}^{2} + 4 {x}^{3} + 20x - 2 {x}^{4} - 10 {x}^{2} }{ {( {x}^{2} - 4x)}^{2} } = \\ = \frac{ {x}^{4} - 8 {x}^{3} - 5 {x}^{2} }{ {( {x}^{2} - 4x) }^{2} }$