derivative of 3sqrt(x)+2/(5x^3-sqrt(2))

解

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

\frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

解答ステップ

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

簡素化

3 x + \frac{2}{5 x ^{3}} - 2 : - 2 + \frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}}

= \frac{d}{d x} (- 2 + \frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}})

和/差の法則を適用:

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

= - \frac{d}{d x} (2) + \frac{d}{d x} (\frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}})

\frac{d}{d x} (2) = 0

\frac{d}{d x} (\frac{2 + 15 x ^{\frac{7}{2}}}{5 x ^{3}}) = \frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

= - 0 + \frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}

簡素化

= \frac{- 12 x ^{2} + 15 x ^{\frac{11}{2}}}{10 x ^{6}}