(d^4)/(dx^4)(1/(1-x))

解

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

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

解答ステップ

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

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

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

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

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

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

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

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

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