derivative of \sqrt[3]{4x}

解

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

\frac{4 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

解答ステップ

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

連鎖法則を適用:

\frac{1}{3 ( 4 x ) ^{\frac{2}{3}}} \frac{d}{d x} (4 x)

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

\frac{d}{d x} (4 x) = 4

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

簡素化

\frac{1}{3 ( 4 x ) ^{\frac{2}{3}}} \cdot 4 : \frac{4 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}

= \frac{4 ^{\frac{1}{3}}}{3 x ^{\frac{2}{3}}}