Question

Решить производную
(Х^2+1)/(x^2-1)

Answer 1

Ответ:

$y = \frac{ {x}^{2} + 1 }{ {x}^{2} - 1 }$

$y' = \frac{( {x}^{2} + 1)'( {x}^{2} - 1) - ( {x}^{2} - 1)'( {x}^{2} + 1) }{ {( {x}^{2} - 1) }^{2} } = \\ = \frac{2x( {x}^{2} - 1) - 2x\times( {x}^{2} + 1) }{ {( {x}^{2} - 1)}^{2} } = \\ = \frac{2x( {x}^{2} - 1 - {x}^{2} - 1)}{ {( {x}^{2} - 1) }^{2} } = \\ = \frac{2x \times ( - 2)}{ {( {x}^{2} - 1)}^{2} } = - \frac{4x}{ {( {x}^{2} - 1) }^{2} }$