Question

Производные. Номер 7

Answer 1

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

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

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

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