derivative of (x^5-6/x ^{-2})

解

\frac{d}{d x} ((x^{5} - \frac{6}{x})^{- 2})

- \frac{2 x ( 5 x ^{6} + 6 )}{( x ^{6} - 6 ) ^{3}}

解答ステップ

\frac{d}{d x} ((x^{5} - \frac{6}{x})^{- 2})

連鎖法則を適用:

- \frac{2}{( x ^{5} - \frac{6}{x} ) ^{3}} \frac{d}{d x} (x^{5} - \frac{6}{x})

= - \frac{2}{( x ^{5} - \frac{6}{x} ) ^{3}} \frac{d}{d x} (x^{5} - \frac{6}{x})

\frac{d}{d x} (x^{5} - \frac{6}{x}) = 5 x^{4} + \frac{6}{x ^{2}}

= - \frac{2}{( x ^{5} - \frac{6}{x} ) ^{3}} (5 x^{4} + \frac{6}{x ^{2}})

簡素化

- \frac{2}{( x ^{5} - \frac{6}{x} ) ^{3}} (5 x^{4} + \frac{6}{x ^{2}}) : - \frac{2 x ( 5 x ^{6} + 6 )}{( x ^{6} - 6 ) ^{3}}

= - \frac{2 x ( 5 x ^{6} + 6 )}{( x ^{6} - 6 ) ^{3}}