derivative of \sqrt[5]{(5x/(4x-3)})

解

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

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

解答ステップ

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

連鎖法則を適用:

\frac{1}{5 ( \frac{5 x}{4 x - 3} ) ^{\frac{4}{5}}} \frac{d}{d x} (\frac{5 x}{4 x - 3})

= \frac{1}{5 ( \frac{5 x}{4 x - 3} ) ^{\frac{4}{5}}} \frac{d}{d x} (\frac{5 x}{4 x - 3})

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

= \frac{1}{5 ( \frac{5 x}{4 x - 3} ) ^{\frac{4}{5}}} (- \frac{15}{( 4 x - 3 ) ^{2}})

簡素化

\frac{1}{5 ( \frac{5 x}{4 x - 3} ) ^{\frac{4}{5}}} (- \frac{15}{( 4 x - 3 ) ^{2}}) : - \frac{3}{5 ^{\frac{4}{5}} x ^{\frac{4}{5}} ( 4 x - 3 ) ^{\frac{6}{5}}}

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