derivative of \sqrt[13]{9+7\sqrt[5]{2x}}

解

\frac{d}{d x} (13 9 + 7 5 2 x)

\frac{7 5 2}{65 x ^{\frac{4}{5}} ( 9 + 7 5 2 5 x ) ^{\frac{12}{13}}}

解答ステップ

\frac{d}{d x} (13 9 + 7 5 2 x)

連鎖法則を適用:

\frac{1}{13 ( 9 + 7 5 2 x ) ^{\frac{12}{13}}} \frac{d}{d x} (9 + 7 5 2 x)

= \frac{1}{13 ( 9 + 7 5 2 x ) ^{\frac{12}{13}}} \frac{d}{d x} (9 + 7 5 2 x)

\frac{d}{d x} (9 + 7 5 2 x) = \frac{7 5 2}{5 x ^{\frac{4}{5}}}

= \frac{1}{13 ( 9 + 7 5 2 x ) ^{\frac{12}{13}}} \cdot \frac{7 5 2}{5 x ^{\frac{4}{5}}}

簡素化

\frac{1}{13 ( 9 + 7 5 2 x ) ^{\frac{12}{13}}} \cdot \frac{7 5 2}{5 x ^{\frac{4}{5}}} : \frac{7 5 2}{65 x ^{\frac{4}{5}} ( 9 + 7 5 2 5 x ) ^{\frac{12}{13}}}

= \frac{7 5 2}{65 x ^{\frac{4}{5}} ( 9 + 7 5 2 5 x ) ^{\frac{12}{13}}}