derivative of \sqrt[4]{8x^2}

解

\frac{d}{d x} (4 8 x^{2})

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

解答ステップ

\frac{d}{d x} (4 8 x^{2})

連鎖法則を適用:

\frac{1}{4 ( 8 x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (8 x^{2})

= \frac{1}{4 ( 8 x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (8 x^{2})

\frac{d}{d x} (8 x^{2}) = 16 x

= \frac{1}{4 ( 8 x ^{2} ) ^{\frac{3}{4}}} \cdot 16 x

簡素化

\frac{1}{4 ( 8 x ^{2} ) ^{\frac{3}{4}}} \cdot 16 x : \frac{1}{2 ^{\frac{1}{4}} x ^{\frac{1}{2}}}

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