(d^5)/(dx^5)(1/(x-1))

解

\frac{d ^{5}}{d x ^{5}} (\frac{1}{x - 1})

- \frac{120}{( x - 1 ) ^{6}}

解答ステップ

\frac{d ^{5}}{d x ^{5}} (\frac{1}{x - 1})

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

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

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

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

\frac{d}{d x} (\frac{2}{( x - 1 ) ^{3}}) = - \frac{6}{( x - 1 ) ^{4}}

= \frac{d ^{2}}{d x ^{2}} (- \frac{6}{( x - 1 ) ^{4}})

\frac{d}{d x} (- \frac{6}{( x - 1 ) ^{4}}) = \frac{24}{( x - 1 ) ^{5}}

= \frac{d}{d x} (\frac{24}{( x - 1 ) ^{5}})

\frac{d}{d x} (\frac{24}{( x - 1 ) ^{5}}) = - \frac{120}{( x - 1 ) ^{6}}

= - \frac{120}{( x - 1 ) ^{6}}