(d^2)/(dx^2)((2x)/(x^2+1))

解

\frac{d ^{2}}{d x ^{2}} (\frac{2 x}{x ^{2} + 1})

- \frac{4 x ( - x ^{2} + 3 )}{( x ^{2} + 1 ) ^{3}}

解答ステップ

\frac{d ^{2}}{d x ^{2}} (\frac{2 x}{x ^{2} + 1})

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

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

\frac{d}{d x} (\frac{2 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}) = - \frac{4 x ( - x ^{2} + 3 )}{( x ^{2} + 1 ) ^{3}}

= - \frac{4 x ( - x ^{2} + 3 )}{( x ^{2} + 1 ) ^{3}}