Question

найдите производную функции (х/(х²+1)

Answer 1

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