(d^2)/(dx^2)((x^2+6x)/(x^2-9))

解

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2} + 6 x}{x ^{2} - 9})

- \frac{6 ( - 2 x ^{3} - 9 x ^{2} - 54 x - 27 )}{( x ^{2} - 9 ) ^{3}}

解答ステップ

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2} + 6 x}{x ^{2} - 9})

\frac{d}{d x} (\frac{x ^{2} + 6 x}{x ^{2} - 9}) = \frac{- 6 x ^{2} - 18 x - 54}{( x ^{2} - 9 ) ^{2}}

= \frac{d}{d x} (\frac{- 6 x ^{2} - 18 x - 54}{( x ^{2} - 9 ) ^{2}})

\frac{d}{d x} (\frac{- 6 x ^{2} - 18 x - 54}{( x ^{2} - 9 ) ^{2}}) = - \frac{6 ( - 2 x ^{3} - 9 x ^{2} - 54 x - 27 )}{( x ^{2} - 9 ) ^{3}}

= - \frac{6 ( - 2 x ^{3} - 9 x ^{2} - 54 x - 27 )}{( x ^{2} - 9 ) ^{3}}