Question

Помогите найти производную.

Answer 1

Ответ:

f)

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

$y't = 1 - \frac{6}{9t} \times 9 = 1 - \frac{6}{t}$

$x't = 6 {t}^{ - 2} = \frac{6}{ {t}^{2} }$

$y'x = \frac{1 - \frac{6}{t} }{ \frac{6}{ {t}^{2} } } = \frac{ {t}^{2} (1 - \frac{6}{t} )}{6} = \\ = \frac{ {t}^{2} - 6t}{6}$

g)

${e}^{xy} - 6x = 0 \\ {e}^{xy} \times (y + xy') - 6 = 0 \\ y {e}^{xy} + xy' {e}^{xy} = 6 \\ xy' {e}^{xy} = 6 - y {e}^{xy} \\ y' = \frac{6 - y {e}^{xy} }{x {e}^{xy} }$

h)

$x {y}^{18} + x = \sin(9y)$

${y}^{18} + 18x {y}^{17} y' + 1 = 9 \cos(9y) \\ 18xy' {y}^{17} = 9 \cos(9y) - 1 - {y}^{18} \\ y '= \frac{9 \cos(9y) - {y}^{18} - 1 }{18x {y}^{17} }$