derivative of 5\sqrt[5]{x^2}-4/x+sqrt(2)

解

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

\frac{2 x ^{2} + 4 x ^{\frac{3}{5}}}{x ^{\frac{13}{5}}}

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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

= \frac{2}{x ^{\frac{3}{5}}} - (- \frac{4}{x ^{2}}) + 0

簡素化

\frac{2}{x ^{\frac{3}{5}}} - (- \frac{4}{x ^{2}}) + 0 : \frac{2 x ^{2} + 4 x ^{\frac{3}{5}}}{x ^{\frac{13}{5}}}

= \frac{2 x ^{2} + 4 x ^{\frac{3}{5}}}{x ^{\frac{13}{5}}}