Question

Знайдіть похідну Yштрих(х)

Answer 1

Ответ:

$y'_x = \frac{y'_t}{x'_t}$

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

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

$y'_x = \frac{1}{ \sqrt{2 t- t {}^{2} } } \times \frac{ \sqrt{2t - t {}^{2} } }{1 - t} = \frac{1}{1 - t}$