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

解

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

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

解答ステップ

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

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

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

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

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