derivative 5/x-2/(x^3)+1/(x^4)

解

導関数

\frac{5}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}}

- \frac{5}{x ^{2}} + \frac{6}{x ^{4}} - \frac{4}{x ^{5}}

解答ステップ

\frac{d}{d x} (\frac{5}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{5}{x}) - \frac{d}{d x} (\frac{2}{x ^{3}}) + \frac{d}{d x} (\frac{1}{x ^{4}})

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

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

\frac{d}{d x} (\frac{1}{x ^{4}}) = - \frac{4}{x ^{5}}

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

簡素化

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