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

解

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

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

解答ステップ

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

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

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

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

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