derivative of \sqrt[4]{2x-1}

解

\frac{d}{d x} (4 2 x - 1)

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

解答ステップ

\frac{d}{d x} (4 2 x - 1)

連鎖法則を適用:

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

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

\frac{d}{d x} (2 x - 1) = 2

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

簡素化

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

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