derivative 3/(x^2)-8\sqrt[4]{x}

解

導関数

\frac{3}{x ^{2}} - 8 4 x

\frac{- 6 x ^{\frac{3}{4}} - 2 x ^{3}}{x ^{\frac{15}{4}}}

解答ステップ

\frac{d}{d x} (\frac{3}{x ^{2}} - 8 4 x)

和/差の法則を適用:

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

= \frac{d}{d x} (\frac{3}{x ^{2}}) - \frac{d}{d x} (8 4 x)

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

\frac{d}{d x} (8 4 x) = \frac{2}{x ^{\frac{3}{4}}}

= - \frac{6}{x ^{3}} - \frac{2}{x ^{\frac{3}{4}}}

簡素化

- \frac{6}{x ^{3}} - \frac{2}{x ^{\frac{3}{4}}} : \frac{- 6 x ^{\frac{3}{4}} - 2 x ^{3}}{x ^{\frac{15}{4}}}

= \frac{- 6 x ^{\frac{3}{4}} - 2 x ^{3}}{x ^{\frac{15}{4}}}