derivative of (1+1/x ^2)

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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