derivative of ((x+2/x)^3+((x-2)/x)^3)

解

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

- \frac{48}{x ^{3}}

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

簡素化

- \frac{6 ( x + 2 ) ^{2}}{x ^{4}} + \frac{6 ( x - 2 ) ^{2}}{x ^{4}} : - \frac{48}{x ^{3}}

= - \frac{48}{x ^{3}}