Question

Найти производную
y=x/x^2+1

Answer 1

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

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

Answer 2

.............................................