Question

Пожалуйста помогите решить очень надо

Answer 1

1. у'=
$= 5 {x}^{4} - 3 + 2 times frac{1}{2 sqrt{x} } - frac{7 times ( - 1)}{ {x}^{2} } = \ = 5 {x}^{4} - 3 + frac{1}{ sqrt{x} } + frac{7}{ {x}^{2} }$
2. f'(x)=(х²+1)'(2х+5)+(2х+5)'(х²+1)=2х(2х+5)+2(х²+1)=4х²+10х+2х²+2=6х²+10х+2

3.
$f'(x) = frac{(3x + 8)'(2x - 1) - (2x - 1)'(3x + 8)}{ {(2x - 1)}^{2} } = \ = frac{3(2x - 1) - 2(3x + 8)}{ {(2x - 1)}^{2} } = \ = frac{6x - 3 - 6x - 16}{4 {x}^{2} - 4x + 1 } = \ = - frac{19}{4 {x}^{2} - 4x + 1}$
4.
sin x= 1/2
x=(-1)ⁿπ/6 + πn, nєZ.

5. (8+2х-6х²)'<5х+2
2-12х<5х+2
-12х-5х<2-2
-17х<0
х>0
хє(0;+∞)