derivative of (5x^3/4-2/(5x^3))

解

\frac{d}{d x} (\frac{5 x ^{3}}{4} - \frac{2}{5 x ^{3}})

\frac{15 x ^{2}}{4} + \frac{6}{5 x ^{4}}

解答ステップ

\frac{d}{d x} (\frac{5 x ^{3}}{4} - \frac{2}{5 x ^{3}})

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{5 x ^{3}}{4}) - \frac{d}{d x} (\frac{2}{5 x ^{3}})

\frac{d}{d x} (\frac{5 x ^{3}}{4}) = \frac{15 x ^{2}}{4}

\frac{d}{d x} (\frac{2}{5 x ^{3}}) = - \frac{6}{5 x ^{4}}

= \frac{15 x ^{2}}{4} - (- \frac{6}{5 x ^{4}})

簡素化

= \frac{15 x ^{2}}{4} + \frac{6}{5 x ^{4}}