derivative of 3x^2+2/x-1/(x^2)

解

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

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

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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

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

簡素化

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