Question

Математика СРОЧНО ПОМОГИТЕ!!!
Номер 9.48,9.49,9.50,9.51

Answer 1

Ответ:

48

$y' = 4 {x}^{3} + 6 {x}^{2} - 2x \\ y'' = 12 {x}^{2} + 12x - 2$

49

$y' = {x}^{2} - x \\ y'' = 2x - 1\\ y'''=2$

50

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

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

51

$y' = ( {x}^{2} )' ln(x) + ( ln(x)) ' \times {x}^{2} = \\ = 2x ln(x) + \frac{1}{x} \times {x}^{2} = \\ = 2x ln(x) + x = x(2 ln(x ) + 1)$

$y'' = 2 ln(x) + 1 + x \times \frac{2}{x} = \\ = 2 ln(x) + 1 + 2 = 2 ln(x) + 3\\y'''=\frac{2}{x}$

Answer 2

Ответ:

Пошаговое объяснение: