derivative of (x^7/7-x^3-3/x+1/(5x^5))

解

\frac{d}{d x} (\frac{x ^{7}}{7} - x^{3} - \frac{3}{x} + \frac{1}{5 x ^{5}})

x^{6} - 3 x^{2} + \frac{3}{x ^{2}} - \frac{1}{x ^{6}}

解答ステップ

\frac{d}{d x} (\frac{x ^{7}}{7} - x^{3} - \frac{3}{x} + \frac{1}{5 x ^{5}})

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{x ^{7}}{7}) - \frac{d}{d x} (x^{3}) - \frac{d}{d x} (\frac{3}{x}) + \frac{d}{d x} (\frac{1}{5 x ^{5}})

\frac{d}{d x} (\frac{x ^{7}}{7}) = x^{6}

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

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

\frac{d}{d x} (\frac{1}{5 x ^{5}}) = - \frac{1}{x ^{6}}

= x^{6} - 3 x^{2} - (- \frac{3}{x ^{2}}) - \frac{1}{x ^{6}}

簡素化

= x^{6} - 3 x^{2} + \frac{3}{x ^{2}} - \frac{1}{x ^{6}}