derivative of \sqrt[3]{1+x^4}

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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