(d^{10})/(dx^{10)}(x/(e^x))

解

\frac{d ^{10}}{d x ^{10}} (\frac{x}{e ^{x}})

- \frac{- x + 10}{e ^{x}}

解答ステップ

\frac{d ^{10}}{d x ^{10}} (\frac{x}{e ^{x}})

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

= \frac{d ^{9}}{d x ^{9}} (\frac{1 - x}{e ^{x}})

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

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

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

= \frac{d ^{7}}{d x ^{7}} (\frac{- x + 3}{e ^{x}})

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

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

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

= \frac{d ^{5}}{d x ^{5}} (\frac{- x + 5}{e ^{x}})

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

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

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

= \frac{d ^{3}}{d x ^{3}} (\frac{- x + 7}{e ^{x}})

\frac{d}{d x} (\frac{- x + 7}{e ^{x}}) = - \frac{- x + 8}{e ^{x}}

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

\frac{d}{d x} (- \frac{- x + 8}{e ^{x}}) = \frac{- x + 9}{e ^{x}}

= \frac{d}{d x} (\frac{- x + 9}{e ^{x}})

\frac{d}{d x} (\frac{- x + 9}{e ^{x}}) = - \frac{- x + 10}{e ^{x}}

= - \frac{- x + 10}{e ^{x}}