(d^6)/(dx^6)(x^{-3})

解答

\frac{d ^{6}}{d x ^{6}} (x^{- 3})

\frac{20160}{x ^{9}}

求解步骤

\frac{d ^{6}}{d x ^{6}} (x^{- 3})

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

= \frac{d ^{5}}{d x ^{5}} (- \frac{3}{x ^{4}})

\frac{d}{d x} (- \frac{3}{x ^{4}}) = \frac{12}{x ^{5}}

= \frac{d ^{4}}{d x ^{4}} (\frac{12}{x ^{5}})

\frac{d}{d x} (\frac{12}{x ^{5}}) = - \frac{60}{x ^{6}}

= \frac{d ^{3}}{d x ^{3}} (- \frac{60}{x ^{6}})

\frac{d}{d x} (- \frac{60}{x ^{6}}) = \frac{360}{x ^{7}}

= \frac{d ^{2}}{d x ^{2}} (\frac{360}{x ^{7}})

\frac{d}{d x} (\frac{360}{x ^{7}}) = - \frac{2520}{x ^{8}}

= \frac{d}{d x} (- \frac{2520}{x ^{8}})

\frac{d}{d x} (- \frac{2520}{x ^{8}}) = \frac{20160}{x ^{9}}

= \frac{20160}{x ^{9}}