Question

Для функций заданных параметрически найти первую производную .

Answer 1

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

$y't = - \frac{2}{3} {(1 - t)}^{ - \frac{5}{3} } \times ( - 1) = \\ = \frac{2}{3 \sqrt[3]{ {(1 - t)}^{5} } }$

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

$y'x = \frac{2}{3(1 - t) \sqrt[3]{ {(1 - t)}^{2} } } \times \frac{ \sqrt{2 t- {t}^{2} } }{1 - t} = \\ = \frac{2 \sqrt{2 t- {t}^{2} } }{3 \sqrt[3]{ {(1 - t)}^{8} } }$