(d^5)/(dx^5)(ln(x+1))

解

\frac{d ^{5}}{d x ^{5}} (ln (x + 1))

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

解答ステップ

\frac{d ^{5}}{d x ^{5}} (ln (x + 1))

\frac{d}{d x} (ln (x + 1)) = \frac{1}{x + 1}

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

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

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

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

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

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

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

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

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