Question

найти производную функции y=(1+x^2)/x

Answer 1

Ответ:

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

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