derivative 5+6/x+6/(x^2)

解

導関数

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

- \frac{6}{x ^{2}} - \frac{12}{x ^{3}}

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (5) = 0

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

\frac{d}{d x} (\frac{6}{x ^{2}}) = - \frac{12}{x ^{3}}

= 0 - \frac{6}{x ^{2}} - \frac{12}{x ^{3}}

簡素化

= - \frac{6}{x ^{2}} - \frac{12}{x ^{3}}