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

解

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

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

解答ステップ

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

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

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

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

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