derivative y= 4/((sqrt(2x))^3)

解

導関数

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

- \frac{3 x ^{2}}{2 x ^{\frac{7}{2}}}

解答ステップ

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

簡素化

\frac{4}{( 2 x ) ^{3}} : \frac{2}{x ^{3}}

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

連鎖法則を適用:

\frac{1}{2 \frac{2}{x ^{3}}} \frac{d}{d x} (\frac{2}{x ^{3}})

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

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

= \frac{1}{2 \frac{2}{x ^{3}}} (- \frac{6}{x ^{4}})

簡素化

\frac{1}{2 \frac{2}{x ^{3}}} (- \frac{6}{x ^{4}}) : - \frac{3 x ^{2}}{2 x ^{\frac{7}{2}}}

= - \frac{3 x ^{2}}{2 x ^{\frac{7}{2}}}