Question

Необходимо найти d^2y/dx^2

Answer 1

Ответ:

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

$y''xx = \frac{(y'x)'t}{xt}$

$y't = \frac{1}{1 + {t}^{2} } \times 2t$

$x't = \frac{1}{1 + {t}^{2} }$

$y'x = \frac{2t}{1 + {t}^{2} } \times (1 + {t}^{2} ) = 2t$

$(y'x)'t = 2$

$y''xx = \frac{2}{ \frac{1}{ 1+ {t}^{2} } } = 2(1 + {t}^{2} ) = 2 + 2 {t}^{2}$