(d^3)/(dx^3)(1/(x^2+1))

解

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

\frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}

解答ステップ

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

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

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

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

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

\frac{d}{d x} (- \frac{2 ( - 3 x ^{2} + 1 )}{( x ^{2} + 1 ) ^{3}}) = \frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}

= \frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}