derivative of-(50/(x^3)+5/(x^2))

解

\frac{d}{d x} (- \frac{50}{x ^{3}} + \frac{5}{x ^{2}})

\frac{150}{x ^{4}} - \frac{10}{x ^{3}}

解答ステップ

\frac{d}{d x} (- \frac{50}{x ^{3}} + \frac{5}{x ^{2}})

和/差の法則を適用:

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

= - \frac{d}{d x} (\frac{50}{x ^{3}}) + \frac{d}{d x} (\frac{5}{x ^{2}})

\frac{d}{d x} (\frac{50}{x ^{3}}) = - \frac{150}{x ^{4}}

\frac{d}{d x} (\frac{5}{x ^{2}}) = - \frac{10}{x ^{3}}

= - (- \frac{150}{x ^{4}}) - \frac{10}{x ^{3}}

簡素化

= \frac{150}{x ^{4}} - \frac{10}{x ^{3}}