(d^6)/(dx^6)(x^{-6})

解

\frac{d ^{6}}{d x ^{6}} (x^{- 6})

\frac{332640}{x ^{12}}

解答ステップ

\frac{d ^{6}}{d x ^{6}} (x^{- 6})

\frac{d}{d x} (x^{- 6}) = - \frac{6}{x ^{7}}

= \frac{d ^{5}}{d x ^{5}} (- \frac{6}{x ^{7}})

\frac{d}{d x} (- \frac{6}{x ^{7}}) = \frac{42}{x ^{8}}

= \frac{d ^{4}}{d x ^{4}} (\frac{42}{x ^{8}})

\frac{d}{d x} (\frac{42}{x ^{8}}) = - \frac{336}{x ^{9}}

= \frac{d ^{3}}{d x ^{3}} (- \frac{336}{x ^{9}})

\frac{d}{d x} (- \frac{336}{x ^{9}}) = \frac{3024}{x ^{10}}

= \frac{d ^{2}}{d x ^{2}} (\frac{3024}{x ^{10}})

\frac{d}{d x} (\frac{3024}{x ^{10}}) = - \frac{30240}{x ^{11}}

= \frac{d}{d x} (- \frac{30240}{x ^{11}})

\frac{d}{d x} (- \frac{30240}{x ^{11}}) = \frac{332640}{x ^{12}}

= \frac{332640}{x ^{12}}