Question

ДАЮ 20 БАЛЛОВ ЗА МАТЕМАТИКУ ПОМОГИТЕ!!!

Answer 1

Ответ:

5

${x}^{2} - 2xy + 2 {y}^{2} + x + 13y - 1 = 0 \\ 2x - 2y - 2xy'+ 1 + 13y' + 0 = 0 \\ y'(13 - 2x) = - 1 - 2x + 2y \\ y' = \frac{2y - 2x - 1}{13 - 2x} \\ \\ y'(2, - 2) = \frac{ - 4 - 4 - 1}{13 - 4} = \frac{ - 9}{9} = - 1$

6

$y'x = \frac{y't}{x't}$

$y't = 3 {e}^{3t}$

$x't = \frac{3}{4} {t}^{ - \frac{1}{4} } = \frac{3}{4 \sqrt[4]{t} }$

$y'x = 3 {e}^{3t} \times \frac{4 \sqrt[4]{t} }{3} = 4 {e}^{3t} \sqrt[4]{t}$

$y'x(1) = 4 {e}^{3} \times 1 = 4 {e}^{3}$