derivative of ((x+1/x)^3)

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

3 (\frac{x + 1}{x})^{2} (- \frac{1}{x ^{2}}) : - \frac{3 ( x + 1 ) ^{2}}{x ^{4}}

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