derivative (a+b/(x^2))^3

解

導関数

(a + \frac{b}{x ^{2}})^{3}

- \frac{6 b ( a x ^{2} + b ) ^{2}}{x ^{7}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

3 (a + \frac{b}{x ^{2}})^{2} (- \frac{2 b}{x ^{3}}) : - \frac{6 b ( a x ^{2} + b ) ^{2}}{x ^{7}}

= - \frac{6 b ( a x ^{2} + b ) ^{2}}{x ^{7}}