Question

Помогите пожалуйста!!! Нужно найти производную:
$y = \frac{x}{ \sqrt{ {x}^{2} - 1 } }$

Answer 1

$y = \frac{x}{ \sqrt{ {x}^{2} - 1 } } \\ \\ y' = \frac{x' \times \sqrt{ {x}^{2} - 1 } - x \times (\sqrt{ {x}^{2} - 1 })' }{ {( \sqrt{ {x}^{2} - 1} )}^{2} } = \\ = \frac{ \sqrt{ {x}^{2} - 1} - x \times \frac{1}{2 \sqrt{ {x}^{2} - 1} } \times 2x}{{( \sqrt{ {x}^{2} - 1} )}^{2} } = \\ = \frac{\sqrt{ {x}^{2} - 1} - \frac{ {x}^{2} }{ \sqrt{ {x}^{2} - 1} } }{{( \sqrt{ {x}^{2} - 1} )}^{2} } = \frac{ \frac{ {x}^{2} - 1 - {x}^{2} }{ \sqrt{ {x}^{2} - 1 } } }{{( \sqrt{ {x}^{2} - 1} )}^{2} } = \\ = - \frac{1}{{( \sqrt{ {x}^{2} - 1} )}^{3} }$