(d^4)/(dx^4)((8x)/(1-x))

解

\frac{d ^{4}}{d x ^{4}} (\frac{8 x}{1 - x})

\frac{192}{( 1 - x ) ^{5}}

解答ステップ

\frac{d ^{4}}{d x ^{4}} (\frac{8 x}{1 - x})

\frac{d}{d x} (\frac{8 x}{1 - x}) = \frac{8}{( 1 - x ) ^{2}}

= \frac{d ^{3}}{d x ^{3}} (\frac{8}{( 1 - x ) ^{2}})

\frac{d}{d x} (\frac{8}{( 1 - x ) ^{2}}) = \frac{16}{( 1 - x ) ^{3}}

= \frac{d ^{2}}{d x ^{2}} (\frac{16}{( 1 - x ) ^{3}})

\frac{d}{d x} (\frac{16}{( 1 - x ) ^{3}}) = \frac{48}{( 1 - x ) ^{4}}

= \frac{d}{d x} (\frac{48}{( 1 - x ) ^{4}})

\frac{d}{d x} (\frac{48}{( 1 - x ) ^{4}}) = \frac{192}{( 1 - x ) ^{5}}

= \frac{192}{( 1 - x ) ^{5}}