derivative \sqrt[3]{5+6x^6}

解

導関数

3 5 + 6 x^{6}

\frac{12 x ^{5}}{( 5 + 6 x ^{6} ) ^{\frac{2}{3}}}

解答ステップ

\frac{d}{d x} (3 5 + 6 x^{6})

連鎖法則を適用:

\frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 + 6 x^{6})

= \frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 + 6 x^{6})

\frac{d}{d x} (5 + 6 x^{6}) = 36 x^{5}

= \frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \cdot 36 x^{5}

簡素化

\frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \cdot 36 x^{5} : \frac{12 x ^{5}}{( 5 + 6 x ^{6} ) ^{\frac{2}{3}}}

= \frac{12 x ^{5}}{( 5 + 6 x ^{6} ) ^{\frac{2}{3}}}