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

解

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

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

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (4 x) = 4

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

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

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

簡素化

= 4 + \frac{3}{x ^{2}} - \frac{2}{x ^{3}}